An Interactive Intelligent Decision Support System for Integration of Inventory

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An Interactive Intelligent Decision Support System for Integration of Inventory,

Planning, Scheduling and Revenue Management

A dissertation presented to

the faculty of

the Russ College of Engineering and Technology of Ohio University

In partial fulfillment

of the requirements for the degree

Doctor of Philosophy

Ehsan Ardjmand

August 2015

This dissertation titled

An Interactive Intelligent Decision Support System for Integration of Inventory,

Planning, Scheduling and Revenue Management

EHSAN ARDJMAND

has been approved for

the Department of Industrial and Systems Engineering

and the Russ College of Engineering and Technology by

Gary R. Weckman

Associate Professor of Industrial and Systems Engineering

Dennis Irwin

Dean, Russ College of Engineering and Technology 3

ABSTRACT

ARDJMAND, EHSAN, Ph.D., August 2015, Mechanical and Systems Engineering

An Interactive Intelligent Decision support system for Integration of Inventory, Planning,

Scheduling and Revenue Management

Director of Dissertation: Gary R. Weckman

The long-term permanency and profitability of a firm requires decisions to be made wisely and on time. For this purpose, it is essential to consider all aspects of a decision in terms of its impact on revenue, planning, scheduling, and inventory in an integrated framework.

In this research paper, an interactive intelligent decision support system for making an integrated decision in the presence of demand uncertainty is proposed. The system operates in a multi-product, multi-period setting, and its objective is to maximize the profit of the firm over time. To achieve its objective, the system first obtains the optimal price and capacity plan for the coming periods. The output of this first step becomes the input for the second step, in which the problem of scheduling is solved. At the end, based on the scheduling step, the optimum inventory policy is determined.

To cope with demand uncertainty in the pricing and planning phase, a robust optimization model is proposed in which the demand is considered to belong to an interval and there is no knowledge (such as statistical distribution) associated with the demand. The robust problem is solved using a metaheuristic.

During the scheduling step, a general setting for the problem is considered, in which each product is treated like a project with a flow network. To address the problem 4 of scheduling, a simulation optimization method is applied in which the optimization step determines the dispatch rule of the jobs and the simulation step schedules the dispatched jobs on the production line.

During the inventory step, the system obtains the best schedule for ordering and storing the raw material in order to minimize the inventory cost. For this purpose, a mixed integer mathematical model is proposed and a metaheuristic is applied to obtain the best solution.

All modules of the proposed decision support system are supported with a database that stores the data obtained from the shop floor and the market. This database is used to assess the costs and parameters in models by applying a cost estimation support system.

To evaluate the effectiveness of the proposed decision support system, it has implemented in a small size textile production line. The data generated by the system and its users are analyzed for a period of four months. Four indicators of profit per product, overall equipment effectiveness, percentage of realized schedule and work-in-progress are monitored during these four months and their values are compared against the same time period in previous year. The results show that the system has improved in terms of profitability, equipment effectiveness and production line control. However, the work-in- progress has not improved. 5

DEDICATION

To my parents and wife, Fereydoon, Tayebeh and Maria

ACKNOWLEDGMENTS

First, I would like to express my sincere gratitude to my advisor Dr. Gary R.

Weckman who helped me greatly in the course of this research. Had it not been for his confidence in me and invaluable guidance that gone far beyond this dissertation, my academic life would have not been possible. I owe him a great many thanks for his support and friendship.

My deepest thanks to Dr. William A. Young for providing me the opportunity to broaden my academic perspective by teaching and involve me in various research projects. His enthusiasm, encouragement, and faith in me have been extremely contributed to this dissertation.

I would also like to thank Dr. Namkyu Park for his brilliant comments and intellectual support. He was always available for my questions and knew where to look for the answers while leading me to the right direction in both theory and practice.

My sincere thanks go to my dissertation committee Dr. Andy Snow and Dr.

Hajrudin Pasic for their thoughtful feedback, which has added value to this research.

Special thanks to Bradly Weckman for his great comments on the manuscript and Dr.

Weckman’s lovely wife, Janet that always supported me spiritually. 7

TABLE OF CONTENTS

Page

Abstract ...... 3

Dedication ...... 5

Acknowledgments...... 6

List of Tables ...... 12

List of Figures ...... 14

1 Introduction ...... 18

1.1 Background ...... 19

1.2 Problem ...... 21

1.3 Significance...... 22

1.4 Implementation and Data Acquisition ...... 22

2 Literature Review ...... 23

2.1 Decision Support Systems (DSS) ...... 23

2.2 Pricing and Revenue Management Systems ...... 28

2.3 Forecasting Support Systems ...... 31

2.4 Cost Estimation Decision Support Systems ...... 38

2.5 Planning and Scheduling Support Systems...... 41

2.6 Inventory Management Systems ...... 50

2.7 Limitations ...... 55

3 General Framework of the System ...... 57

3.1 Cost Estimation ...... 58 8

3.2 Pricing and Planning ...... 58

3.3 Scheduling...... 59

3.4 Inventory ...... 59

4 Financial and Cost Estimation Module ...... 60

4.1 Inputs...... 60

4.1.1 Cost Centers ...... 60

4.1.2 Costs ...... 61

4.2 Processes ...... 62

4.2.1 Estimating Finished Costs ...... 62

4.2.2 Estimating Inventory Costs ...... 63

4.2.3 Estimating Lost Sale Cost ...... 64

4.3 Design and Outputs of Finance and Cost Estimation Module ...... 64

5 Pricing and Planning Module ...... 66

5.1 Inputs...... 66

5.1.1 Inputs from Finance and Cost Estimation Module ...... 67

5.1.2 Resource Constraints ...... 67

5.1.3 Demand and Uncertainty ...... 67

5.2 Processes ...... 70

5.2.1 Robust Optimization ...... 74

5.2.2 Non-linear Model ...... 76

5.2.3 Linear Model ...... 78

5.2.4 Robust Model ...... 80

5.2.5 Solution Methods ...... 82

5.2.5.1 Exact Method ...... 83 9

5.2.5.2 Unconscious Search ...... 83

5.2.5.3 Applying an Unconscious Search to Pricing and Planning Module ..... 94

5.2.5.4 Verification of Unconscious Search Results...... 96

5.3 Design and Outputs of Pricing and Planning Module ...... 98

6 Scheduling Module ...... 100

6.1 Inputs...... 100

6.1.1 Inputs from Pricing and Planning Module ...... 100

6.1.2 Timeline and Working Hours ...... 101

6.1.3 Machines ...... 101

6.1.4 Maintenance ...... 103

6.1.5 Stations ...... 103

6.1.6 Setup Times ...... 103

6.1.7 Operators and Skill Levels ...... 104

6.1.8 Operation Chart ...... 104

6.2 Processes ...... 105

6.2.1 Scheduling ...... 106

6.2.1.1 Scheduling One Job ...... 109

6.2.1.2 Optimizing Dispatching Rule Using Variable Neighborhood Search 113

6.2.2 Control ...... 116

6.3 Design and Outputs of Scheduling Module ...... 118

7 Inventory Management Module ...... 120

7.1 Inputs...... 120

7.1.1 Inputs from Scheduling Module ...... 120 10

7.1.2 Inventory Holding Cost ...... 121

7.1.3 Bill of Material (BOM) ...... 121

7.1.4 Suppliers and Material Specifications ...... 121

7.2 Processes ...... 122

7.2.1 Mathematical Model ...... 122

7.2.2 Solution Methods ...... 124

7.2.2.1 Exact Solution ...... 125

7.2.2.2 Hybrid Tabu Search and Simplex Algorithm ...... 125

7.2.2.3 Verification of Hybrid Algorithm ...... 128

7.3 Design and Outputs of Inventory Management Module ...... 129

8 Experimentation ...... 131

8.1 Introducing the Textile Factory and Shop Floor ...... 131

8.2 Introducing the Products ...... 147

8.3 Estimating the Costs and Resource Constraints...... 153

8.4 Pricing, Planning and Price of Robustness ...... 155

8.5 Scheduling...... 163

8.6 Inventory Management ...... 166

8.7 Performance Evaluation of the System ...... 173

8.7.1 Profit per Product ...... 174

8.7.2 Overall Equipment Effectiveness (OEE) ...... 176

8.7.3 Percentage of Realized Schedule ...... 177

8.7.4 Work-in-Progress (WIP) ...... 178

9 Concluding Remarks and Future Works ...... 180 11

9.1 Financial and Cost Estimation Module ...... 181

9.2 Pricing and Planning Module...... 181

9.3 Scheduling...... 182

9.4 Inventory Management ...... 183

9.5 Implementation ...... 183

9.6 Limitations and Generalizability...... 184

9.7 Future Works ...... 185

References ...... 187

Appendix A: Cplex Code for Pricing and Planning Module ...... 222

Appendix B: Simplex Code Used in Pricing and Planning Module ...... 227

Appendix C: Work Profile Database ...... 232

Appendix D: Machine and Maintenance Database ...... 233

Appendix E: Cplex Code for Inventory Management Module ...... 234

LIST OF TABLES

Page

Table 1. DSS interaction taxonomy (Haettenschwiler, 2001) ...... 27

Table 2. DSS use taxonomy (D. Power, 2002) ...... 27

Table 3. Categorization of pricing and revenue management systems in manufacturing

literature based on different types of DSSs...... 30

Table 4. Different types of forecasting support systems designed for different forecasting

issues ...... 34

Table 5. Different types of DSSs designed based on various cost estimation methods ... 40

Table 6. Different types of planning support systems designed for different scheduling

and planning problems ...... 45

Table 7: Different types of planning support systems designed for different inventory

problems’ level...... 52

Table 8: The time (hour) each product spent on each cost center and the total expenses

recorded in each cost center (CC) ...... 63

Table 9: Share of each product in each cost center and its finished cost...... 63

Table 10: Test problems’ specifications used for evaluation of unconscious search ...... 97

Table 11: Solution quality and run time of exact and US algorithms for six artificially

generated test problems; for each instance, US has run 10 times ...... 98

Table 12. Six randomly generated test problems for verifying the hybrid algorithm..... 128 13

Table 13. Solution quality and run time of exact and hybrid algorithms for six artificially

generated test problems where for each instance the hybrid algorithm has run 10

times ...... 129

Table 14: Price points for each product in each period, suggested by sales department 148

Table 15: The min. and max. demand for each product per price point in period 1 ...... 149

Table 16: The min. and max. demand for each product per price point in period 2 ...... 150

Table 17: The min. and max. demand for each product per price point in period 3 ...... 151

Table 18: The min. and max. demand for each product per price point in period 4 ...... 152

Table 19: Estimated production, inventory, and lost sale costs for products ...... 154

Table 20: Prices obtained by pricing and planning module for each period ($)...... 156

Table 21: Production plan obtained by pricing and planning module ...... 157

Table 22: Production plan for worst-case scenario ...... 161

Table 23: Chosen prices for each product in each period for the worst-case scenario ... 162

Table 24: Fabric consumption for each product (yard) ...... 168

Table 25: Purchasing cost of each fabric from different suppliers ...... 169

Table 26: Consumption of each fabric in each period ...... 170

Table 27: Material plan for each fabric that needs to be ordered by a specific supplier in

periods 1 and 2 ...... 171

Table 28: Material plan for each fabric that needs to be ordered by a specific supplier in

periods 3 and 4 ...... 172

LIST OF FIGURES

Page

Figure 1. Evolution and progress of DSSs in time ...... 26

Figure 2. Areas of revenue management in manufacturing ...... 29

Figure 3. Design, selection/specification and evaluation issues in forecasting (adopted

from (Winklhofer et al., 1996))...... 34

Figure 4. Different methods of cost estimation and their application in different stages of

product development (adopted from Duverlie and Castelain (1999)) ...... 39

Figure 5. Complexity hierarchy of scheduling problems based on machine environments

(adopted from (Pinedo, 2012)) ...... 42

Figure 6. complexity hierarchy of scheduling problems based on processing

properties/constraints (adopted from (Pinedo, 2012)) ...... 43

Figure 7. complexity hierarchy of scheduling problems based on objective functions

(adopted from (Pinedo, 2012)) ...... 43

Figure 8. Information flow chart in manufacturing (adopted from (Pinedo, 2012)) ...... 45

Figure 9. General framework and modules of the proposed decision support system ..... 57

Figure 10. Relation of costs, cost types and cost centers ...... 61

Figure 11. Inputs, processes and outputs of finance and cost estimation modules ...... 65

Figure 12. A Schematic diagram of relation of demand and price for a specific product

and period where each bar shows the minimum and maximum of demand for

different values of price ...... 69

Figure 13. Translation function and measurement matrix...... 88 15

Figure 14. Functions of and for the situation where there are two decision variables,

and ...... 93

Figure 15. Flow chart of applying unconscious search to pricing and planning module . 96

Figure 16. A prototype of pricing and planning interface ...... 99

Figure 17. Inputs, processes and outputs of the pricing and planning module ...... 99

Figure 18. The lean time remains after subtracting the repair and inefficient times plus

the amount of time a machine is producing defective products ...... 102

Figure 19. A prototype of an operation chart consisting of six stages ...... 105

Figure 20. General framework of the heuristic used in a scheduling module ...... 109

Figure 21. A product’s operation chart and its critical path ...... 110

Figure 22. a) original timeline b) timeline after scheduling task A ...... 111

Figure 23. Flowchart of scheduling a single job ...... 113

Figure 24. VNS algorithm for finding the best sequence of jobs for scheduling ...... 115

Figure 25. Schematic domain model of the database for a control process in terms of the

scheduling module ...... 118

Figure 26. Inputs, processes and outputs of a scheduling module ...... 119

Figure 27. Flowchart of the hybrid tabu search and Simplex algorithm applied to the

inventory management problem ...... 127

Figure 28. Input and outputs of inventory management module ...... 130

Figure 29. The material needed and activities involved in “support” station for producing

coat 832 ...... 133

Figure 30. Support station standard configuration ...... 134 16

Figure 31. The materials needed and activities involved in “front” station for producing

coat 832 ...... 135

Figure 32. Front station standard configuration ...... 136

Figure 33. The materials needed and activities involved in “back” station for producing

coat 832 ...... 136

Figure 34. Back station standard configuration ...... 137

Figure 35. The materials needed and activities involved in “sleeve” station for producing

coat 832 ...... 138

Figure 36. Standard configuration of sleeve station ...... 138

Figure 37. The materials needed and activities involved in “hem” station for producing

coat 832 ...... 139

Figure 38. Standard configuration of hem station ...... 139

Figure 39. The materials needed and activities involved in “lining” station for producing

coat 832 ...... 140

Figure 40. Standard configuration of lining station ...... 141

Figure 41. The materials needed and activities involved in “collar” station for producing

coat 832 ...... 142

Figure 42. Standard configuration of collar station ...... 142

Figure 43. The materials needed and activities involved in “body assembly” station for

producing coat 832 ...... 143

Figure 44. Standard configuration of body assembly station ...... 143 17

Figure 45. The materials needed and activities involved in “supplementary lining” station

for producing coat 832 ...... 144

Figure 46. Standard configuration of supplementary lining station ...... 144

Figure 47. The materials needed and activities involved in “supplementary 1” station for

producing coat 832 ...... 145

Figure 48. Standard configuration of a supplementary 1 station ...... 145

Figure 49. The materials needed and activities involved in “supplementary 2” station for

producing coat 832 ...... 146

Figure 50. Standard configuration of supplementary 2 station ...... 146

Figure 51. Overall shop floor layout ...... 147

Figure 52. Increase in profit as the production capacity increases ...... 158

Figure 53. Price of robustness per different values of uncertainty budget parameter .... 160

Figure 54. User interface for defining operation process of coat 832 ...... 164

Figure 55. User interface for defining the jobs and choosing the objective function .... 165

Figure 56. User interface for scheduling November 8th, 9th., and 10th ...... 166

Figure 57. Value of the objective function vs. warehouse capacity ...... 173

Figure 58. OEE of production line before and after implementing the system ...... 177

Figure 59. Percentage of realized schedule before and after implementing the system . 178

1 INTRODUCTION

In recent decades, as the competition among companies has become fiercer, there has been an increasing need for solutions which can support and guarantee the profitability and permanency of companies in the market. Hence, decision support systems have become the focus of varied research as a part of information systems domain. These are the models that can analyze a massive amount of data in the shortest possible time and help managers to make decisions according to highly fluctuating situations of the market.

Decision Support Systems (DSS), as the intersection of management science and information systems, are “the application of available and suitable computer-based technology to help improve the effectiveness of managerial decision making in semi- structured tasks” (Keen & Morton, 1978). DSSs have been applied to facilitate decision making processes in various problem areas in manufacturing such as revenue management, planning, scheduling, inventory, and pricing. However, the integration of all related problems observed in manufacturing in order to support a predetermined strategy in companies has remained overlooked in literature.

The focus of this research is on proposing an interactive intelligent decision support system capable of cost estimation, planning, the scheduling of jobs and the workforce, and in determining inventory policy. This is all based on the interaction with an expert on the price of products and the corresponding market behavior in terms of sales volume for different periods. The overall goal of the proposed DSS is to maximize 19 the revenue of a manufacturing plant while considering the constraints of capacity, the workforce, and the warehouse.

To show the applicability and efficiency of the DSS, a real case in the textile industry will be chosen as a pilot and the improvement of the plant, in terms of revenue, is measured after the implementation of the system. The case of the textile industry has been chosen due to its highly fluctuating demand, which makes it difficult to predict the behavior of the market; hence, it is a hard task to simultaneously consider all the related problems of pricing, planning, scheduling, and inventory. The proposed DSS can be applied to every similar manufacturing plant where productions are separate and discrete and it is difficult to predict the patterns of demand.

1.1 Background

There is a vast body of scholarly research in literature on the application of decision support systems in manufacturing. Various DSS frameworks have been proposed for different domains such as forecasting, pricing, cost estimation, revenue management, planning, scheduling, and inventory. In DSS literature, each of these problems is addressed based on two factors--namely, the DSS type used and the problem specifications and boundaries.

In terms of DSSs, there are two categorizations in literature. From one perspective, DSSs have three different types; active, cooperative, and passive

(Haettenschwiler, 2001). Active DSSs propose a solution for a specific problem explicitly. Cooperative DSSs suggest solutions while cooperating with the decision maker(s), and passive DSSs are not designed to suggest a solution explicitly. 20

From another perspective, DSSs are classified in five groups--namely, communication driven, data driven, document driven, knowledge driven, and model driven (D. Power, 2002). Communication driven DSSs are mostly based on the interaction between users and the system. Data driven and document driven DSSs have a primary objective to retrieve relevant data in real time based on historical records or existing documents. Knowledge driven DSSs take advantage of expert knowledge. Model driven DSSs apply mathematical models to find solutions for a problem, mostly in terms of optimization.

The problems which DSSs are mostly used to deal with are of a semi-structured nature (Er, 1988; Ren, Zhang, & Zhang, 1997; Trefil, 2001). However, structured and unstructured problems can also be the focus of DSSs. Structured problems are those with a well-defined nature, where there is no ambiguity and the method for solving the problem is available. Semi-structured problems are those of a high complexity, for which there is no unique solution but there is a general agreement on system evaluation and solution. Unstructured problems are usually ambiguous in nature, where there is no consensus on the data representation and the solution method. These problems need to be interactively analyzed by a group of experts (Er, 1988; Trefil, 2001).

Based upon the settings of the problem, revenue management, pricing, cost estimation, planning, scheduling, and inventory related issues could be of a semi- structured or structured nature. In reality, due to many factors involved, these problems are difficult to address, and hence are considered semi-structured. The difficulty of these problems becomes even more apparent when the dependency of them is taken into 21 account. Most of the existing literature on DSSs and these problems consider them separate and isolated areas. However, these areas are highly dependent and hence, rendering decisions about only one of them at a time may not be the best idea for the whole system.

There are few publications which integrate more than one area when it comes to revenue management, pricing, cost estimation, planning, scheduling, and inventory. This research attempts to design a comprehensive DSS framework which integrates all aforementioned problems while interacting with experts on the probable behavior of the market when a decision is supposed to be made.

1.2 Problem

The overall objective of this research is to propose an intelligent, interactive decision support system for the integration of revenue management, pricing, cost estimation, planning, scheduling, and inventory based upon the interaction with experts and mathematical models for maximizing the profit over multiple periods in a manufacturing plant.

To support the overall objective of the research, some sub-objectives have to be met. These include: 1) designing a model for the interaction of system and expert; 2) designing a model for a pricing decision; 3) modeling the planning problem; 4) modeling the scheduling problem,;5) designing a cost estimation procedure; 6) modeling inventory;

7) integrating all of the decisions; 8) designing a software framework for the proposed

DSS; and 9) implementing the DSS. 22

To measure the efficiency of the proposed DSS, it has been implemented in a textile manufacturing plant. The results of running the DSS have been evaluated in terms of revenue improvement and production throughput.

1.3 Significance

A DSS development that integrates revenue management, pricing, cost estimation, planning, scheduling, and inventory based upon the interaction with an expert can improve the profitability of a manufacturing plant, and also supports the goals of the plant in terms of its permanency in the market. Among manufacturing industries, textiles will be tested in this research; however, the proposed DSS can be applied to various industries with separable and discrete production processes and fluctuating demand patterns.

1.4 Implementation and Data Acquisition

To test the effectiveness of the proposed decision support system, a small size textile production line with 30 products has chosen. The system is implemented and the data of four months, starting from November 1st 2014 up to March 1st 2015 is analyzed and compared against the same period in previous year. The criteria of comparison are profit per product, overall equipment effectiveness, percentage of realized schedule and the work-in-progress. The input and output of each module of the system implemented, along with a detailed explanation of the production line and products are described in section 8‎ .

2 LITERATURE REVIEW

In this section, a brief review of DSSs is stated, and the application of DSSs in related manufacturing domains is reviewed by considering the different types of DSSs and problem specifications. Limitations of research in each area are also reviewed in each section, with an overall conclusion at the end.

2.1 Decision Support Systems (DSS)

Decision Support Systems (DSS) are a part of the Information Systems (IS) domain, in which the main focus is on providing support for decision making at the managerial level (Arnott & Pervan, 2005; Farbey, Land, & Targett, 1995). Since the first appearance of the term “decision support system” in an article by Gorry and Scott Morton

(1971), there has been no consensus on a universal definition (Er, 1988), though some researchers have tried to propose one. For example, Keen and Scott Morton (1978) define

DSS as “the application of available and suitable computer-based technology to help improve the effectiveness of managerial decision making in semi-structured tasks”.

DSSs are generally designed to deal with structured, semi-structured, and unstructured problems (Er, 1988; Ren et al., 1997; Trefil, 2001). Structured problems are those with a well-defined nature, where there is no ambiguity and the method for solving the problem is available. Semi-structured problems are those of a high complexity for which there is no unique solution, but there is a general agreement on system evaluation and solution. Unstructured problems are usually ambiguous in nature, where there is no consensus on the data representation and solution method for them and they need to be interactively analyzed by a group of experts (Er, 1988; Trefil, 2001). These types of 24 problems can be observed in different levels of management activities such as operational control, management control, and strategic planning. For instance, in a management control level setting, production level, the starting budget, and the decision whether or not to hire a new manager are considered to structured, semi-structured, and unstructured problems, respectively (Er, 1988). In order to deal with problems of different natures – i.e. structured, semi-structured, and unstructured – DSSs need to have six main functionalities. These functions include the selection of data, aggregation of data, and the parameters’ estimation for distribution functions, as well as simulation, equalization, and optimization (Blanning, 1979; Fowler & Rose, 2004).

The first information systems were developed to assist automation of different operations—such as inventory and accounting—in organizations in the 1960s (Arnott &

Pervan, 2005). However, due to a lack of proper understanding of the managerial process by IT practitioners, most of them turned out to be a failure (Ackoff, 1967; Dearden, 1972;

Tolliver, 1971). The first appearance of the term “decision support system” was in an article by Gorry and Scott Morton (1971). The aim of this paper was to improve the experience of managerial bodies in using information systems by proposing a framework based on the management activities. After these early works, the research area of DSSs remained fairly theoretical and experimental for more than a decade (Alter, 1980).

Later on, different concepts and elements were introduced and incorporated into

DSSs which lead to development of a set of new information systems. These systems included personal decision support systems (Alter, 1980), group support systems (Huber,

1984), negotiation support systems (Rangaswamy & Shell, 1997), intelligent decision 25 support systems (Bidgoli, 1998), Executive Information Systems and Business

Intelligence (Rockart & De Long, 1988), data warehouses (Cooper, Watson, Wixom, &

Goodhue, 2000), and Knowledge Management-based Decision Support Systems (Alavi

& Leidner, 2001). Introduction of new concepts and information systems related to DSSs has been consistent with advancements in technology, business environments, the decision making process, and information technology. Hence, many frameworks for designing and implementing DSSs have been developed and improved since its conceptualization(Alavi & Henderson, 1981; Bui & Lee, 1999; Gorry & Morton, 1971;

March & Hevner, 2007; Metaxiotis, Psarras, & Samouilidis, 2003; Phillips-Wren, 2009;

D. J. Power, 2000; SHARIT, EBERTS, & SALVENDY, 1988; Sprague, 1980; W. E.

Walker et al., 2003). From this point of view, DSS is not a unified and static domain

(Arnott & Pervan, 2005). Figure 1, adopted from Arnott and Pervan (2005), shows the evolution of different DSSs in their time and origin.

Figure 1. Evolution and progress of DSSs in time

DSSs can be categorized according to two criteria of interaction and use (Alves, da Silva, & Varela, 2013). The first taxonomy, shown in Table 1 and adopted from Bihl et al. (2013), is proposed by Haettenschwiler (2001) and based on human interaction. It divides DSSs into active, cooperative, and passive types. The second taxonomy, summarized in Table 2 and adopted from Bihl et al. (2013), is based on use, and divides

DSSs into those which are communication driven, data driven, document driven, knowledge driven, or model driven (D. Power, 2002).

Table 1. DSS interaction taxonomy (Haettenschwiler, 2001) Type Description

Active  Provide suggestions or state solutions to complex problems

 Most complicated

 Require the most interaction between the DSS and the human decision-

makers

Cooperative  Iterative approach:

1. Provide example solution

2. User modifies system parameters

3. DSS refines until arrival at a compromised solution

Passive  Not designed to determine a solution explicitly for decision-makers

Table 2. DSS use taxonomy (D. Power, 2002) Type Description

Communication Driven  Provide information to groups working on shared tasks

 Emphasize retrieval of real-time (or historic) internal or Data Driven (extra data)

 Integrates collected stored and processing technologies to Document Driven assist a decision maker with information retrieval

 Derive specific recommendations for decision makers from Knowledge Driven computer-driven and expert information

 Provide insight from mathematical models on perceived Model Driven phenomena

DSSs have been widely employed in corporate functional and non-corporate applications (H. B. Eom & Lee, 1990; S. Eom & Kim, 2005; S. B. Eom, Lee, Kim, &

Somarajan, 1998). Corporate functional applications DDSs have been used in include finance (Serrano-Cinca & Gutiérrez-Nieto, 2013), human resources (Broderick &

Boudreau, 1992), marketing (P. S. Balakrishnan, Jacob, & Xia, 2010), inventory

(Achabal, McIntyre, Smith, & Kalyanam, 2000), scheduling (L. Lin, Cochran, & Sarkis,

1992), forecasting (Guo, Wong, & Li, 2013), transportation (Y. Liu et al., 2010), production (Tabucanon, Batanov, & Verma, 1994), and strategic management (Cebeci,

2009).

DSSs also have a variety of applications in non-corporate cases such as agriculture (J. Liu, Wu, Tao, & Chu, 2013), education (Litvin et al., 2012), government

(Shan, Wang, Li, & Chen, 2012), healthcare (Beliën, Demeulemeester, & Cardoen,

2009), military (Song, Ryu, & Kim, 2010), natural resources (Newton, 2012), and urban/community planning (Poole, Courtney, Lomax, & Vedlitz, 2009). In the rest of this section, the application of DSSs in revenue management, forecasting, cost estimation, planning and scheduling, and inventory will be investigated in more detail and the limitations of existing literature will be examined.

2.2 Pricing and Revenue Management Systems

Revenue management is a field in which the focus is on maximizing revenue by managing factors such as price and the distribution channels of goods and services

(Chiang, Chen, & Xu, 2007). The first applications of revenue management date back to around 45 years ago in the airline industry (Chiang et al., 2007), and gradually have 29 found their way to many other areas such as hospitality industries (Kimes, 2005), health care (Lieberman, 2004), retailing (Tsai & Hung, 2009), and manufacturing (Barut &

Sridharan, 2005).

Revenue management problems in manufacturing can be classified into three major areas; market analysis, capacity planning, and pricing (Cheraghi, Dadashzadeh, &

Venkitachalam, 2010). In market analysis, the focus is on market segmentation and forecasting. In capacity planning, inventory management and planning/scheduling are mostly discussed. In pricing, based on the configuration of the system – i.e. make-to- stock or make-to-order – the pricing techniques are the main concern. Figure 2 shows the related areas of revenue management in manufacturing.

Figure 2. Areas of revenue management in manufacturing

Literature related to market analysis and capacity planning – i.e. forecasting, planning/scheduling and inventory management – will be discussed in future sections. In this section, the focus will be on pricing decision support systems.

Following the categorization of DSSs by Power (2002) that were introduced in the previous section, Table 3 summarizes the literature of pricing and revenue management systems in manufacturing.

Table 3. Categorization of pricing and revenue management systems in manufacturing literature based on different types of DSSs Communication Document Knowledge Data Driven Model Driven Driven Driven Driven

(Green &

(Hilton, Krieger, 1992)

Swieringa, & (Krasteva,

Turner, 1988) Singh, Sotirov, (Singh, 1991) (Bennavail, Bennavail, & (Casey & Harding, & Mincoff, 1994) Murphy, 1994) Spears, 1990) (Albers, 1996)

(Woo, Levy, & (Cassaigne &

Bible, 2005) Singh, 2001)

(Yan, 2011)

As it can be observed from Table 3 , most of the literature involved in the application of DSSs for pricing in manufacturing is in data- and model-driven DSSs. In 31 data-driven DSSs, the focus is on the historical data available from the past. In model- driven DSSs, developing mathematical models that justify the relationship between pricing and the inventory or sales amount are the main concern. In knowledge-driven

DSSs, expert systems have been used to choose the right price for products.

Reviewing Table 3 reveals some of the gaps and limitations of the literature. For example, despite the potential usage advantages of communication-driven DSSs in regards to pricing, these systems have not been investigated in this area. Also, the integration of pricing and capacity planning is not completely investigated in literature.

Integration of pricing, the different aspects of capacity planning in a manufacturing firm, and other related processes such as cost estimation continue to remain the main limitations and gaps in literature in terms of the application of DSSs in pricing for manufacturing.

2.3 Forecasting Support Systems

Although the forecasting problem is not tackled in this research directly, since a part of the proposed decision support system receives the forecasted demand from the expert, a brief literature review regarding forecasting support systems is included.

Within a manufacturing company, forecasting issues can be categorized into three domains of design; selection, specification and evaluation issues (Winklhofer,

Diamantopoulos, & Witt, 1996). In each category there are some key elements for a decision maker to decide about. In design, common questions include:

 What is the purpose of forecasting? 32

 How frequently should the forecasting be conducted, and what is

the time horizon of forecasting?

 What kind of resources do we need?

 Who should do the forecasting?

 Who is going to use the results?

 What are the data resources?

In selection and specification, one has to deal with questions such as:

 What forecasting method can be applied?

 Is it necessary to use multiple techniques?

At the evaluation level, a decision maker may face questions such as:

 How can a forecast result be displayed and presented for

management?

 Is it necessary to take into account the subjective judgment of

experts about forecasting? If yes, how?

 What metrics are needed for forecasting evaluations?

 How is it possible to address the forecasting problem more

efficiently and improve it?

An answer to each one of these questions can have a great impact on the profit of a manufacturing plant in terms of internal factors such as capacity usage, inventory costs, workforce assignment, etc., and external factors such as market share and stock price

(Hirst, Koonce, & Venkataraman, 2008; Mahmoud, Rice, & Malhotra, 1988; Raturi,

Meredith, McCutcheon, & Camm, 1990; Wright, 1988). For finding a suitable answer to 33 these issues, it is necessary to take advantage of existing models, such as time series, artificial neural networks, and expert judgment (Fildes, Nikolopoulos, Crone, & Syntetos,

2008; Goodwin, Fildes, Lawrence, & Nikolopoulos, 2007; Lawrence, O'Connor, &

Edmundson, 2000; Webby, O'Connor, & Edmundson, 2005; Winklhofer &

Diamantopoulos, 2003). Figure 3, adopted from (Winklhofer et al., 1996), depicts these issues and their corresponding domains and topics of decision making.

A forecasting support system (FSS) is a software framework which takes advantage of expert judgment, mathematical techniques, and past data integration in order to assist decision makers in forecasting and analyzing the results (Adya & Lusk,

2012; Armstrong, 2001; Fildes, Goodwin, & Lawrence, 2006). In other words, FSS is where DSS meets forecasting techniques. In this sense, FSSs can also be classified based on DSSs and forecasting issues. Table 4 summarizes various research conducted in FSSs in manufacturing. 34

Figure 3. Design, selection/specification and evaluation issues in forecasting (adopted from (Winklhofer et al., 1996))

Table 4. Different types of forecasting support systems designed for different forecasting issues DSS Type Design Selection/Specification Evaluation

(Cheikhrouhou, Communication Marmier, Ayadi, & Driven Wieser, 2011)

Data Driven

Document Driven

Table 4: continued (R. Kuo & Xue, 1998) (Petrovic, Xie, (R. Kuo, 2001) Knowledge Driven (Wen, 2007) & Burnham, (R. J. Kuo, Wu, & 2006) Wang, 2002)

(Caliusco, (Korpela & Tuominen, Villarreal, 1996) Toffolo, (Venkatachalam & Sohl, Taverna, & 1999) Chiotti, 1998) (Winklhofer & (Thomassey, Happiette, (Zhong, Pick, Diamantopoulos, 2003) & Castelain, 2005) Klein, & Jiang, (Sun, Choi, Au, & Yu, (J. D. Bermúdez, 2005) 2008) Segura, & Vercher, (Dellarocas, (Ching-Chin, Ka Ieng, 2006) Model Driven Zhang, & Ling-Ling, & Ling- (J. D. Bermúdez, Awad, 2007) Chieh, 2010) Segura, & Vercher, (Ali, Sayın, (Xia, Zhang, Weng, & 2007) Van Woensel, Ye, 2012) (J. Bermúdez, Segura, & & Fransoo, (Guo et al., 2013) Vercher, 2008) 2009) (C.-T. Lin & Lee, 2009) (Efendigil, (Sayed, Gabbar, & Önüt, & Miyazaki, 2009) Kahraman,

2009)

Table 4: continued (Corberán-Vallet,

Bermúdez, Segura, &

Vercher, 2010)

(Poler & Mula, 2011)

(Wagner, Michalewicz,

Schellenberg, Chiriac, &

Mohais, 2011)

(Y. Yu, Choi, & Hui,

2011)

(Aksoy, Ozturk, &

Sucky, 2012)

(J. D. Bermúdez,

Segura, & Vercher,

2012)

According to the publications reviewed in Table 4 , the most investigated area is in the application of model-driven DSSs in selection and specification issues in forecasting. Among the different types of DSSs applied, no application regarding the data-driven and document-driven DSSs has been found, and only one publication addresses the communication-driven DSSs. The second area of focus has been on knowledge-driven DSSs. Although various research has been dedicated to FSSs, there are some limitations and gaps which will be stated briefly. 37

Design issues in forecasting mostly address fundamental questions such as the purpose of forecasting, time horizon definition, and data sources selection. Most of the problems faced in this domain are semi-structured or unstructured. For example, it is hard to structurally answer the question, “What data sources can be used for prediction?”

Hence, the models developed in literature for this purpose are limited and mostly focused on time horizon definition. On the other hand, the opinion of an expert seems to be of high value in this domain, and so the importance of communication-driven DSSs become more obvious. However, a limited number of publications have considered this issue.

Considering the nature of design issue in forecasting, integration also seems to be a significant need. There are a few research papers dedicated to this subject, and in all of them, only the integration with marketing is considered (Cheikhrouhou et al., 2011;

Winklhofer & Diamantopoulos, 2003).

The same limitations and gaps already mentioned for design are observed with selection and specification – i.e. a lack of communication-driven DSSs involving application and integration. Additionally, the scope of the concept of selection and specification in most of the research is considered in only a limited format. For example, model selection in most of the papers is bound to a selection of parameters of a specific method—such as exponential smoothing—but no research is dedicated to any comparison between different methods, such as artificial neural networks and time series.

Lack of proper integration and usage of communication-driven DSSs is also a part of the limitations and gaps in evaluating forecasting issues. The amount of research 38 focused on integration is limited, and the integration doesn’t consider design issues

(Caliusco et al., 1998).

In general, three major limitations and gaps can be found regarding FSS research in literature. The first limitation corresponds to the application of communication-driven

FSSs, which can have a high potential in improving the FSSs due to the incorporation of expert opinion. Second, enough integration has not been addressed in literature, and there a lot of missing chains between FSSs and other organizational processes which can be explored and established. Third, due to the complexity of decisions made by FSSs, any comparison between different methods is not considered in each domain.

2.4 Cost Estimation Decision Support Systems

Cost estimation covers a wide spectrum of manufacturing systems, from the feasibility and evaluation of new products to the after-sale services (Layer, Brinke,

Houten, Kals, & Haasis, 2002). There are four basic methods for cost estimation-- namely, intuitive, analogical, parametric, and analytical methods (Duverlie & Castelain,

1999). In an intuitive method, the cost of a product is estimated based on the expert’s knowledge. In an analogical method, the cost of a product is estimated based upon the cost of similar products. The parametric method takes advantage of a product’s parameters and uses them to evaluate the cost. In an analytical method, the emphasis is on the works required to build a product.

Each of these cost estimation methods can be applied in different phases of product development. Figure 4, adopted from Duverlie and Castelain (1999), depicts the application of each cost estimation method to a different phase of product development. 39

As one can observe, parametric methods are more often used in early stages of product development, while analytic methods are mostly used in later phases. Analogical methods are used in both early and later phases. Intuitive methods can be applied in all stages.

Figure 4. Different methods of cost estimation and their application in different stages of product development (adopted from Duverlie and Castelain (1999))

In order to review the literature of cost estimation decision support systems, different methods of cost estimation and different types of DSSs will be considered.

Table 5 lists the existing literature regarding DSSs, based on various cost estimation methods.

Table 5. Different types of DSSs designed based on various cost estimation methods DSS Type intuitive Analogical Parametric Analytical

Communication

Driven

(Koonce, Judd, (Eaglesham,

Sormaz, & 1998)

Masel, 2003) (Ben-Arieh,

(Mauchand, 2000)

Siadat, Bernard, (Park &

Data Driven & Perry, 2008) Simpson*,

(Quintana & 2005)

Ciurana, 2011) (Dai,

(Darla & Balabani, &

Narayanan, Seneviratne,

2013) 2006)

Document

Driven

(Chin & Wong,

1996)

(Kingsman & de (SOUZA & Knowledge (Rush & Roy, (De Souza, 1995) Souza, 1997) KINGSMAN, Driven 2001) (Bode, 1998) 1999)

(Shehab &

Abdalla, 2001)

Table 5: continued (Brinke, 2002)

(H. Wang,

Ruan, & Zhou,

2003)

(Wasim et al.,

2013)

Model Driven

As one can observe from Table 5, most of the research existing in literature belongs to parametric- and analytic-based methods of cost estimation. Only a few publications are devoted to intuitive and analogical methods. Additionally, the most common types of DSSs used in cost estimation are data-driven and knowledge-driven

DSSs.

Most of the publications in cost estimation are solely devoted to cost estimation, and only a few of them consider the integration of cost estimation with other related areas such as pricing and scheduling. Usage of model-driven DSSs also remains largely ignored in literature.

2.5 Planning and Scheduling Support Systems

Scheduling and sequencing play a significant role in manufacturing, and are considered to be an important aspect of decision making on the shop floor (Pinedo,

2012). Generally speaking, the goal of scheduling is to arrange and sequence the jobs on different machines in order to optimize resource consumption (Pinedo, 2012). A 42 scheduling problem is defined by a triplet where is representative of the machine environment, describes processing properties and constraints, and shows the objective (Pinedo, 2012). Scheduling problems can be categorized into two major categories--deterministic and stochastic. The complexity of scheduling problems is measured based upon the three parameters of , , and . Figure 5 depicts the complexity of classification scheduling problems, based on machine environment. 1 stands for a single machine, represents identical machines in parallel, shows machines in parallel with different speeds, stands for unrelated machines in parallel, is flow shop, is flexible flow shop, is job shop, is flexible job shop, and is open shop (Pinedo, 2012).

Figure 5. Complexity hierarchy of scheduling problems based on machine environments (adopted from (Pinedo, 2012))

The same complexity hierarchy can be drawn for processing properties, constraints, and objective functions. Figure 6 shows the complexity hierarchy for processing properties and constraints where is release date, is preemption, is precedence constraints, is sequence dependent setup time, is job families, 43

is batch processing, is breakdown, is machine eligibility restrictions, is permutation, is blocking, is no wait, and is recirculation (Pinedo, 2012).

Figure 6. complexity hierarchy of scheduling problems based on processing properties/constraints (adopted from (Pinedo, 2012))

Figure 7 depicts the complexity hierarchy based on objective functions, where

is maximum lateness, ∑ is the total weighted completion time, ∑

is the discounted total weighted completion time, ∑ is the total weighted tardiness, and ∑ is the weighted number of tardy jobs (Pinedo, 2012).

Figure 7. complexity hierarchy of scheduling problems based on objective functions (adopted from (Pinedo, 2012))

In order to investigate the application DSSs have in scheduling problems, one needs to use a framework for the categorization of scheduling problems where 44 importance of data is also taken into account. Unfortunately, since the focus of the traditional scheduling classification is more on theoretical aspects rather than applicability and information (Framinan & Ruiz, 2010), it cannot be used for exploring

DSSs’ application in scheduling completely, and only a few papers have proposed DSSs based upon traditional classification (Adler et al., 1993; Belz & Mertens, 1996; Josef

Geiger, 2011; Kungwalsong & Kachitvichyanukul, 2006; Viviers, 1983). On the other hand, due to the high complexity of real world scheduling systems, it is often hard to induct them into one of the traditional categories. For these reasons, the focus of this research will be on the information flow diagram proposed by Pinedo (2012), in which scheduling is considered to be a part of more comprehensive schema of planning and scheduling. Figure 8 shows an information flow diagram in a manufacturing system. The chart is composed of three main parts--namely planning, scheduling and dispatching, and shop floor management and control. Application of DSSs in scheduling and planning can be also be categorized by following this diagram.

Figure 8. Information flow chart in manufacturing (adopted from (Pinedo, 2012))

Table 6 summarizes various research conducted on PSSs, keeping in mind the industry type and categorization of DSSs proposed by Power (2002).

Table 6. Different types of planning support systems designed for different scheduling and planning problems Shop floor DSS Type Planning Scheduling management/control

General: General: Communication

Driven (F. T. Chan, Jiang, & (Makarouni, Psarras, Tang, 2000) & Siskos, 2013)

Table 6: continued Agricultural Engine: Communication

Driven (Özdamar, Bozyel, & Birbil, 1998) General: General: (De Vin, Ng, (Grabot, Blanc, & Oscarsson, & Andler, Binda, 1996) 2006) Comp. Man. Wood: Systems: Data Driven (Buehlmann, Ragsdale, & Gfeller, (P. Chen & Talavage, 2000) 1982) (Dilts, Boyd, &

Whorms, 1991) Semi-conductor:

(Fordyce, Dunki‐ Jacobs, Gerard, Sell, & Sullivan, 1992) Document Driven General: General: (Bistline Sr, Banerjee, & (Kan & Chen, 2013) Banerjee, 1998) (K.-S. Wang, Hsia, & (Jindal et al., 2013) Zhuang, 1995) (W.-H. Kuo &

Hwang, 1998) (Novas & Henning,

2009) Knowledge Driven (Shaw, 1988) (Tsadiras, Papadopoulos, & O’Kelly, 2013) (Yamaha, Matsumoto, & Tomita, 2008) Power Plants:

(Aoyagi, Tanemura, Matsumoto, Eki, & Nigawara, 1988)

Table 6: continued Food: Knowledge Driven (Henning & Cerdá, 2000) General: General: General:

(Belz & Mertens, (McConnell & (Borenstein, 1998) 1996) Medeiros, 1992) Electronics: (Escudero, Kamesam, (Josef Geiger, 2011) King, & Wets, 1993) (L. Lin et al., 1992) (Kungwalsong & (Kapanoglu & Kachitvichyanukul, Miller, 2004) 2006) (Mallya, Banerjee, & (Kazerooni, Chan, &

Bistline, 2001) Abhary, 1997) (McKay & Wiers, (Kim & Kim, 1994) 2003) (Tsubone, Matsuura, (H. Li, Li, Li, & Hu,

& Kimura, 1995) 2000) Wood: (Madureira, 2005) (Farrell & Maness, 2005) Appliances: (Mahdavi, Shirazi, & Model Driven (Gazmuri & Arrate, Solimanpur, 2010) 1995) Ship building: (Trentesaux, Dindeleux, & Tahon, (Lee et al., 1995) 1998) Textile: (Tsukiyama & Mori,

(Mok, Cheung, Wong, 1991) Leung, & Fan, 2013) (Viviers, 1983) (Wiendahl &

Garlichs, 1994) (M.-F. Yang & Lin,

2009) Packaging:

(Adler et al., 1993) Ion Plating:

(F. T. Chan, Au, & Chan, 2006) 48

Table 6: continued Refinery:

(Chryssolouris, Papakostas, & Mourtzis, 2005) Steel:

(Cowling, 2003) (Karumanasseri &

Abourizk, 2002) (Tamura, Nagai, Nakagawa, Tanizaki, & Nakajima, 1998) Chemical: Model Driven (Escudero et al., 1993) Electronics:

(Jeong, Leon, & Villalobos, 2007) Turbine

Manufacturing:

(Krishna, Mahesh, Dulluri, & Rao, 2010) Pottery:

(Petrovic & Duenas, 2006) Tobacco:

(Van Dam, Gaalman, & Sierksma, 1998)

The investigation of research published regarding the application of DSSs in scheduling and planning is summarized in Table 6 . Here one can see the variety of DSS types used in literature to address the subject of scheduling and planning. Among the different types of DSSs, to the best of our knowledge, there has been no document-driven 49

DSS applied to scheduling and planning, which seems justified, if one considers the description of this type of DSS listed in Table 2 and the nature of scheduling and planning. Among the other DSSs, most practices belong to model-driven and knowledge- driven DSSs which seems reasonable if one takes into account the well-defined nature of scheduling/planning.

Among various levels of the problematic domain – i.e. planning, scheduling, and shop floor management/control – the least investigated and the most investigated levels are control and scheduling, respectively. Since the application of control systems is limited due to the availability of the data for real-time decision making, most of the research in this area is related to data-driven DSSs. Most of the application-based research is reported in the scheduling and planning level. Although much research has been conducted regarding the application of DSSs in planning and scheduling, there are still some gaps and limitations one finds in the literature, which will be discussed briefly.

In planning, most of the research is focused on model-driven DSSs, which, when one considers the long-term and semi-structured nature of planning and the axiomatic management role in DSSs, it seems that there has been not enough research in communication-driven DSS application. This drawback will become clearer when one considers the planning issue as a problem where many different experts need to get involved in order to create the best outcome.

Additionally, a good plan should be feasible and consistent with other decisions such as scheduling, forecasting, inventory, and marketing in an organization. In this regard, the integration of planning with other systems becomes favorable. However, in 50 literature not much research has focused on this issue (Kungwalsong &

Kachitvichyanukul, 2006; Lee et al., 1995; Özdamar et al., 1998), and the only integration is between planning and scheduling.

Another drawback of literature in this regard is a lack of probabilistic considerations in planning, which due to its medium- to long-term time horizon, seems necessary to consider. In addition, no mechanism was introduced for a correction of the plan when there has been a deviation from the goal.

Like planning, the scheduling literature also suffers from a lack of integration and correction procedures. Furthermore, since the scheduling problem has a short-term horizon and hence, real time data may be important, it seems that data-driven DSSs can be investigated further in this domain.

In spite of planning and scheduling, most of the research on shop floor management/control is integrated with scheduling (P. Chen & Talavage, 1982; Dilts et al., 1991; Fordyce et al., 1992; Grabot et al., 1996; Kan & Chen, 2013; K.-S. Wang et al.,

1995), but there is still not a complete integration between control, scheduling, and planning.

In general, the integration of planning and scheduling support systems with other processes in an organization, probabilistic considerations, and correction procedures remain the main drawback and literature gap in this domain.

2.6 Inventory Management Systems

Inventory problems can be categorized into three different levels; namely, strategic, tactical, and operational (Peidro, Mula, Poler, & Lario, 2009; Rouwenhorst et 51 al., 2000), which cover long-term, medium-term, and short-term decision making for planning, respectively (Gupta & Maranas, 2003).

At the strategic level, the questions that should be addressed include:

 How should one design process flow?

 What type of technical systems should be selected and how?

At the tactical level, a decision maker may face the questions including:

 How does one do dimensioning of the storage system?

 How does one define the layout?

 What kind of equipment should be selected?

 How should one design the organization of inventory?

At the operational level, the problems are of a short-term nature, such as:

 How does one fine tune the organization’s policies?

 How does one assign a work force to different tasks?

 How does one sequence pickings? How does one assign docks for

shipping?

In order to investigate the role of decision support systems in inventory, the same categorization – i.e. strategic, tactical, and operational – will be used. Table 7 summarizes various research conducted in inventory and DSSs. The same classification of DSSs used for planning and scheduling is copied here (D. Power, 2002).

Table 7: Different types of planning support systems designed for different inventory problems’ level DSS Type Strategic Tactical Operational

(Achabal et al., 2000) Communication (P.-C. Yang & Wee, Driven 2006) (Chande, Dhekane, Hemachandra, & (Natarajan, 1989) Rangaraj, 2005) (Banerjee &

Banerjee, 1992) (Kagami, Homma, Akashi, Aizawa, & Mori, 1992) (Manthou & Data Driven Vlachopoulou, 2001) (Moole & Korrapati,

2004) (Van Donselaar, van Woensel,

Broekmeulen, & Fransoo, 2006) Document Driven (Prasad, Shah, & Knowledge Driven (Ehrenberg, 1990) Hasan, 1996) (Tu et al., 2007) (Moynihan, Raj, (Retzlaff-Roberts & Sterling, & Nichols, (Williams, 1984) Amini, 1998) 1995) (Cohen, Kamesam, (Min, 2009) (Sobotka, 1998) Kleindorfer, Lee, & Tekerian, 1990) (Badri, 1999) (Agrell, 1995) (Chaudhry, (Disney, Naim, & Salchenberger, & Towill, 2000) Beheshtian, 1996) (H.-G. Chen & Sinha, Model Driven (J. Walker, 2000) 1996) (H.-h. YU & SUN, (Towill, Evans, &

2002) Cheema, 1997) (Samanta & Al- (Razi & Tarn, 2003) Araimi, 2001) (Disney & Towill, (Signorile, 2005) 2005) (Cheng & Chou, (Woo et al., 2005) 2008)

Table 7: continued (Goel & Gutierrez, (Qingsong & Lizhi,

2006) 2010) (Lo, 2007) (Zeng, Wang, &

Zhang, 2007) (Cakir & Canbolat,

2008) (S. Li & Kuo, 2008) (Shang, Tadikamalla, Model Driven Kirsch, & Brown, 2008) (Southard &

Swenseth, 2008) (Yazgı Tütüncü, Aköz, Apaydın, & Petrovic, 2008) (Zhang, Hua, & Xu,

2009) (Borade & Bansod,

2011) (Cadavid & Zuluaga,

2011)

Review of research tabulated in Table 7 shows that most of the research on the application of DSSs for inventory belong to model-driven DSSs and on the tactical level of decision making. Among the DSSs, there has been no example found of document- driven DSSs in literature. Most of the research is dedicated to model-driven and data- driven DSSs. At the strategic level, only one research paper has been found. At the tactical level, where the problems are well-defined and structured, the focus has been on model -riven DSSs, while at the operational level (where the problems are usually of a short-term nature), most of the research was concentrated on data-driven DSSs. Notice that since in short-term decision making the accessibility of the data is important, data- driven DSSs play a more important role. 54

Although much research has been dedicated to the application of DSSs in inventory, there are some limitations and gaps, which will be discussed briefly.

Inventory problems tend to be semi-structured or unstructured at the strategic level, and hence naturally need expert opinion. In this sense, knowledge-driven and communication-driven DSSs may be of great help. However, this issue has not been covered in literature. Additionally, reviewing the problem at a strategic level demands a strong integration with other units of the organization, such as the production, marketing, tactical, and operational levels. No research considering this issue has been found in this literature review. The applicability of literature on DSSs at the strategic level of inventory decision making also remains an open investigation.

Similar to the strategic level, at the tactical level the literature also suffers from the lack of comprehensive integration. However, unlike at the strategic level, more research has been conducted regarding communication-driven DSSs. Since the decisions in this level are medium-term and still of a semi-structured nature in some areas, the application of expert knowledge seems to be of great help, though this has not been explored comprehensively in literature.

A lack of comprehensive integration also remains a limitation regarding the application of DSSs at the operational level of inventory. Perhaps the only level in which the usage of document-driven DSSs seems to be justified in an inventory is at the operational level. The reason can be the need for documents, which have to be issued for each transaction in inventory. This issue has not been addressed in literature. 55

2.7 Limitations

A review of decision support systems’ (DSS) history, evolution, taxonomy, and application in planning/scheduling, forecasting, and inventory for manufacturing was proposed. Different levels of problems for planning/scheduling, forecasting, and inventory was investigated according to the taxonomy offered by literature. The limitations and gaps of research in this area literature were also briefly explored.

In pricing and revenue management, integration with other related areas of manufacturing such as cost estimation, scheduling, and inventory, as well as the lack of exploration in communication-driven DSSs, remain the main gaps and limitations in literature.

In planning and scheduling, there was a lack of enough research regarding the applications of communication-driven and knowledge driven-DSSs, proper and comprehensive integration, testing, probabilistic considerations, and correcting procedures.

In forecasting, the main limitations and gaps were lack of enough research in the applications of communication-driven and knowledge-driven DSSs, proper and comprehensive integration, applicability and real world testing in many cases, and of considering various models for decision making.

In cost estimation (a particularly important activity in manufacturing), integration with other relevant areas such as pricing, planning, scheduling, inventory, and marketing has not been explored enough in literature. 56

Regarding inventory, lack of enough research in the application of communication-driven, knowledge-driven and document-driven DSSs; lack of a proper and comprehensive integration; lack of applicability and enough testing in much of the research; lack of probabilistic considerations; and lack of correcting procedures remain the main limitations and gaps in literature.

3 GENERAL FRAMEWORK OF THE SYSTEM

In this section the general framework of the system is described. The proposed decision support system has four modules. The output of each module can be the input to another module. Figure 9 depicts the General framework and modules of the proposed decision support system.

Pricing and Planning Demand Prediction Expert Robust Inventory Level and Costs Optimization Warehouse

Cost Estimation Cost of Products Flow Process Chart Analytical Cost Plan Estimation Data Base Skill Level Flow Process Chart

Plan

Scheduling Activities Simulation Flow Process Chart Optimization

Inventory

Mathematical Schedule Shop Floor Modeling

Capacity and Lead Times

Figure 9. General framework and modules of the proposed decision support system

The proposed system is interactive in the sense that it is able to suggest new solutions based on the data it obtains from the shop floor and the demand information that it receives from the expert interactively. The data acquired from the shop floor and 58 the warehouse is stored in a database. The structure of this database will be covered partially in next chapters wherever necessary.

3.1 Cost Estimation

The first module of the system is cost estimation. This module estimates the finished costs, inventory cost and the lost sale cost for each product. The inputs of this module are the cost occurred and the cost centers defined by the user. Cost centers are the entities that store the expenses. For instance, a machine in production line can be a cost center. All the expenses related to purchase, maintenance and operation of each machine are stored in the cost center associated with that machine and will be used to calculate the finished cost of the products that use that machine. This module is explained in detail in section 4‎ .

3.2 Pricing and Planning

The outputs of cost estimation module are used in pricing and planning module for obtaining the optimum set of prices and production plan for each product in each period. In pricing and planning module the demand is considered to be uncertain and price dependent. For this purpose, for each price point a minimum and maximum demand is defined by the expert. To incorporate the uncertainty of the demand in the decision making process, a robust optimization model will be formulated for the problem. This model will be solved using an exact method and a metaheuristic named unconscious search (US). This module is explained in detail in section ‎5. 59

3.3 Scheduling

The output of pricing and planning module will be used in scheduling module.

This part of the system schedules the jobs created by pricing and planning. For this purpose, a simulation optimization method is used in which the processing time of the jobs in each working station is considered probabilistic. Scheduling module tries to obtain the best sequence of jobs on the production line using a variable neighborhood search (VNS). To schedule a single job, it is simulated on the production line several times and the tasks that appear on the critical path are given higher priority for scheduling. This module is explained in detail in section 6‎ .

3.4 Inventory

The last module of the system is inventory. This module tries to minimize the inventory costs using a mathematical model and the inputs from scheduling and pricing and planning modules. To solve the mathematical model of the inventory, an exact method and a tabu search are applied. This module is explained in detail in section 7‎ .

4 FINANCIAL AND COST ESTIMATION MODULE

The decision support system introduced in this research has several modules. In this chapter, the financial and cost estimation module is introduced, and its inputs, processes, methods, and outputs are described.

4.1 Inputs

The financial and cost estimation module has several inputs. Each input comes from an interaction of a user with a system or another module. The inputs of the system are described in the following sub-sections.

4.1.1 Cost Centers

The first inputs of financial and cost estimation modules are cost centers. Any department or unit that a cost may charge into is considered a cost center. Here, two types of cost centers are differentiated. The first type of cost center is an overhead. An overhead cost center is any type of cost center that has the expenses unrelated to direct labor and material included. Such cost centers include human resources and insurance.

Note that the overhead definition can be different based on the business type and products. Since production-based businesses are dealt with in this research, the overhead definition is also adjusted according to the needs of the type of business.

Beside overhead cost centers, there are operational cost centers in which the expenses related to direct labor and direct material are recorded. These types of cost centers include working stations, operators, production machines, work-in-process, and materials purchased.

4.1.2 Costs

Other inputs of financial and cost estimation modules are the costs. A cost has many components, including the amount, date, and type. The amount and date of the cost help to determine the finished costs of products in a period. The type of cost helps to distinguish between operational costs and preparing the balance sheets. To record a cost, one needs to categorize it according to a predefined hierarchy. In practice, this hierarchy has at least three levels/ledgers. The first level shows to which major category an expense belongs, while the other two levels make the categorization more detailed. Figure 10 shows the relation of costs, cost types, and cost centers. To record a cost, one needs to know to which cost center and cost type it belongs. Storing a cost in this format helps to estimate various cost coefficients such as inventory, production, and lost sales cost. In addition, this architecture enables a user to generate different reports based upon his/her needs.

Figure 10. Relation of costs, cost types and cost centers

4.2 Processes

Having costs and cost centers as inputs, the financial and cost estimation module includes three main processes. These processes are estimating finished costs, inventory costs, and lot sale costs, based on an analytical cost estimation method. These three expenses are used as outputs to a pricing and planning module of the decision support system.

4.2.1 Estimating Finished Costs

To estimate the finished cost of a product, it is necessary to know which cost centers are used to produce one unit of that product. It is possible that a cost center will be used for several products. In this case, each product will get a share of the common cost center, based upon the time it has spent in there. As an example, assume a situation in which there are five products and five cost centers. Each cost center has some expenses recorded in it, and each product has used a certain amount of time in each cost center.

Table 8 summarizes the time (hour) each product has spent in each cost center (CC) and the total expenses recorded in each cost center. For calculating the finished cost, the expenses in each cost center should be divided by the time-share of each product from that cost center. Then, all the expenses of that product are added together. Thus, product

1, which has time share of cost center 1, will absorb

of total expenses of CC1. Table 9 shows the share of each product in each cost center and its associated finished cost. Note that these calculations need to be done for each time period.

Table 8: The time (hour) each product spent on each cost center and the total expenses recorded in each cost center (CC) CC 1 CC 2 CC 3 CC 4 CC 5

Prod. 1 22 21 18 12 16

Prod. 2 15 16 12 18 13

Prod. 3 21 15 24 23 14

Prod. 4 22 20 12 17 19

Prod. 5 12 22 16 18 11

Total expenses($) 1200 4500 1600 3200 2400

Table 9: Share of each product in each cost center and its finished cost CC 1 CC 2 CC 3 CC 4 CC 5 Finished Cost

Prod. 1 287.0 1005.3 351.2 436.4 526.0 2605.9

Prod. 2 195.7 766.0 234.1 654.5 427.4 2277.7

Prod. 3 273.9 718.1 468.3 836.4 460.3 2756.9

Prod. 4 287.0 957.4 234.1 618.2 624.7 2721.4

Prod. 5 156.5 1053.2 312.2 654.5 361.6 2538.1

4.2.2 Estimating Inventory Costs

For estimating the inventory cost, the hierarchical structure of the costs can be used. For this purpose, each category in each level of the hierarchy can be marked with the attribute of its inventory cost. This means that if a cost falls under a certain category, its immediate level or its predecessor on the hierarchy is marked as inventory cost, and it will be calculated towards inventory cost. For calculating the total inventory cost, all 64 these categories and the expenses recorded in them will be summed up. Obviously, the inventory cost for a single unit is the total inventory cost divided by the total number of units. Inventory cost can then be determined more precisely if the space occupied by each product is also taken into account.

4.2.3 Estimating Lost Sale Cost

Estimating the lost sale cost is rather straightforward. In this research, the lost sale cost is considered to be the profit that could be made by selling one unit of a product, but was not made due to inventory level. For estimating this number, one needs to know the finished cost and minimum expected profit of a product. In the case where the demand is always greater than the production capacity, the lost sale cost tends to be 0. In the case where lost sales can have dramatic effects on profitability, such as the cases in which there are huge penalties for the late delivery of a product, the lost sale cost can be set to infinity.

4.3 Design and Outputs of Finance and Cost Estimation Module

Financial and cost estimation modules have three main outputs; namely, finished costs, inventory costs, and lost sale costs. These three parameters are very important in building the models for the pricing and planning of products. Figure 11 shows the inputs, processes, and outputs of finance and cost estimation modules.

Figure 11. Inputs, processes and outputs of finance and cost estimation modules

5 PRICING AND PLANNING MODULE

In this chapter, the pricing and planning module is explained in detail and the inputs, processes, and outputs of the module are described. A robust optimization methodology is applied for dealing with demand uncertainty. Since in real world situations the dimension of the problem becomes very large and thus hard to tackle with an exact method, a metaheuristic is introduced to solve large-scale pricing and planning problems. The solutions of metaheuristics are verified by comparing to exact solutions obtained using CPLEX Optimization Studio 12.3.

5.1 Inputs

The pricing and planning module has three sets of inputs. The first set is the outputs of finance and cost estimation modules. The second set is the constraints of resources, such as budget and space. The third set is the time periods and demands obtained from experts. It is assumed that the expert uses a forecasting technique according to his need, and hence the forecasting problem is not tackled in this research.

Rather, it is considered to be handled by the expert and interactively communicated to the system. This assumption makes the system more flexible in the sense that the expert can choose his/her specific method of forecasting, which is more compatible with the business type and its market. In addition, with any change in the demand pattern, the proposed decision support system can come up with a new strategy to improve the profitability. 67

5.1.1 Inputs from Finance and Cost Estimation Module

The first set of inputs to a pricing and planning module comes from the finance and cost estimation module. As mentioned in chapter 4‎ , a finance and cost estimation module has three outputs; namely, finished costs, inventory costs, and lost sale costs.

These values are very important in determining the optimal price and production plan.

When the inventory cost of a product is high, it is expected to be stored in a way where one has the minimum possible inventory at the end of each time period. When the lost sale cost of a product is high, a higher inventory level is expected in order to reduce the probability of lost sales.

5.1.2 Resource Constraints

In order to have an optimum plan, it is necessary to evaluate the constraints regarding the resources such as production capacity, budget, warehouse capacity, workforce availability, and skill level. For this purpose, the maximum possible production level, total budget assigned to each time period, warehouse capacity, space occupied by each product, skill-specific man-hours needed for producing one unit of each product, and the total available work force need to be introduced into the system as inputs.

5.1.3 Demand and Uncertainty

Forecasting and pricing are highly dependent. In literature, the relation between the price of a product and its demand is considered to have the Cobb-Douglas form of

in which is demand, is base demand, is the elasticity constant, and is price (Viswanathan & Wang, 2003). Although this form of demand function is widely 68 accepted in literature, it does not reflect the opinion of a domain expert. Hence, in this research the relation between demand and price will be established by an expert. For this purpose, by using a graphical interface an expert will be asked to define the relationship between demand and price. Information shared by the expert includes the estimated minimum and maximum of demand for different prices and time periods. Figure 12 shows an example of the relationship of demand and price drawn by an expert for a specific product and period. Each bar shows the minimum and maximum of demand for different price values.

This type of representation of the relationship between demand and price has several advantages. These advantages include:

 Interactive: The expert can quantify his knowledge in an

interactive manner by adding, deleting, sharing, and modifying the existing

information.

 Dynamic and flexible: Based on the new information derived from

the market, the expert can change this information and define new points for

the relationship between price and demand.

 Abnormal demand and price relation: In reality, the relationship

between demand and price may have abnormal patterns for different

products. This type of quantification can be used to generate various and

diverse patterns and non-uniform elasticity. 69

 Discounts: It is convenient to quantify discounts and represent

them in the proposed format. Hence, for different periods it is possible to

control salvage prices.

 Managing uncertainty: One important aspect of this representation

is the method by which uncertainty is included. For each price, the expert can

choose an interval for demand by defining the minimum and maximum

possible values of demand.

Figure 12. A Schematic diagram of relation of demand and price for a specific product and period where each bar shows the minimum and maximum of demand for different values of price

The optimal price for a product in a specific period can be calculated using the information fed to the system by the expert. For this purpose, after fixing the price on a specific value, the respective demand intervals will be used as an uncertain parameter for deriving the planning schema for the related period. The importance of representing the demand in the form of an interval is the usage of this interval in using robust optimization techniques in the planning module. 70

5.2 Processes

The main process of pricing and planning modules is to determine the optimal price and plan of production. In practice, these two decisions are usually made separately.

However, solving these two problems simultaneously can improve the quality of solutions.

Pricing, as one of the decisions with a high impact on the profitability of a firm, has always been a debatable issue among researchers and practitioners. In a study conducted by Zbaracki et al. (2004), it is shown that the cost of adjusting the price can eat up to approximately 20% of the net margin. Other studies also show the high impact of pricing decisions on profitability (Levy, Bergen, Dutta, & Venable, 1997; Slade, 1998).

Conventionally, the pricing decision is made by considering the marginal costs of production. However, it can be shown that considering only marginal costs on pricing can result in poor decisions and less profit (Robinson & Lakhani, 1975). Hence, it is essential to determine the price of products while having a broader perspective of the firm’s processes, such as production and inventory planning. Even using an integrated model of planning-pricing with limited demand information can result in better decisions in terms of profitability when compared with simple cost-based pricing (R. Balakrishnan &

Sivaramakrishnan, 2001).

One of the decisions heavily related to pricing is production planning (Federgruen

& Heching, 1999). There is a large body of research on simultaneous production planning and pricing. A comprehensive review and analysis of the problem is proposed by Chan et al. (2004). In their research, the problem of production planning and pricing is 71 categorized according to the length of horizon, dynamic of prices, demand type, demand functional form, demand input parameters, sales, restocking, production setup cost, capacity limits, and products.

In this research, a special case of demand type is considered in which the demand is uncertain – with no knowledge of statistical distribution – and is cost sensitive. For each period, multiple candidate price points with possible minimum and maximum demands associated with it are introduced, among which a single price for each period will be chosen. This type of price-demand definition is very useful when there is not enough information about the reaction of the market to different prices and/or the decision maker just wants to examine a limited set of prices. This method of price- demand definition is also very practical in terms of modeling where a product needs to be sold with a lower price after a certain time. By this approach, the sales expert or decision maker has a lot of flexibility in terms of modeling the different patterns of price-demand and can take various factors into consideration such as seasonality, competition, and demand sensitivity without knowing the distribution of the demand. A robust optimization approach will be applied to incorporate this type of demand and the

“unconscious search” (Ardjmand & Amin-Naseri, 2012) metaheuristic will be used as the solution method. So far there have been several research papers released in the domain of simultaneous pricing and planning.

Kunreuther and Schrage (1973) modeled the problem of joint planning and pricing with a single product, multi-period setting–for each order processed, there was a fixed cost associated. In their research, the demand is considered to have a deterministic 72 curve in each period. They proposed a fast-converging algorithm for solving the problem, taking into consideration a fixed price for the product in each period. However, they suggested that using a variable pricing policy could increase the profitability.

Federgruen and Heching (1999) addressed the problem of single product, multi- period joint pricing and inventory replenishment under demand uncertainty, where the demand is a function of price. In their model, sellouts were considered to be backlogged.

They solved the problem in two cases, using a finite and infinite number of periods and proposing a value iteration method. In addition to their basic model, they also analyzed the effect of lead times, price change bounds, and order size on the problem.

Gilbert (1999) proposed a model for the planning and pricing of a single product with seasonal demand, where the proportion of demand values in different periods are independent of prices and there is a fixed setup cost associated with each period. He developed a procedure for solving the problem which was capable of obtaining the optimal solution.

Balakrishnan and Sivaramkrishnan (2001) considered the problem of planning and pricing in a hierarchical setting, where pricing and planning would be done in two separate phases and the solution could be revised when extra information about demand became available. Gox (2002) considered the planning and pricing problems of a monopolist with uncertain demand. He modeled two types of capacity constraints-- namely soft and hard, where which soft constraints could be violated at a cost, but hard ones could not be violated. 73

Geunes et al. (2006) proposed a model for planning and pricing in the presence of order selection flexibility. They considered a single-period model where the demand could change with price. In their model, the production capacity was considered unlimited. Smith et al. (2009) formulated a single product, joint planning and pricing problem with capacity and inventory constraints. Their solution process consisted of two steps. In the first step, they solved the single-period problem in a precise manner, and in the second step they used this solution to solve the multi-period problem by dynamic programming.

Chen and Hu (2012) addressed the joint inventory planning and pricing problem, where the demand was deterministic and the cost of adjusting the price was high. They proposed a polynomial time algorithm as the solution method, which worked based upon the longest path problem in graphs. Mardaneh and Cacceta (2013) proposed the problem of planning and pricing in a multi-period and multi-product setting with backorders. They formulated the problem in terms of non-linear programming and proposed a method of solution for calculating the optimal price and production amount in a finite time horizon.

Chen et al. (2014) proposed a model for the situation where two types of make-to-order and make-to-stock products were produced and the demand was price-sensitive. In their model, the excess demand was backlogged or lost.

In the literature, when the demand is considered to be price-sensitive, it is usually assumed that if the price is known, then the demand can be determined. In reality, even when one knows the price, there can still be a lot of deviation in demand. Additionally, in many cases it is not possible to determine a function which relates the demand to price, 74 so in these cases only a few different options for price are available. The reasons behind this research are the uncertainty of the demand when even the price is determined, as well as the complexity of estimating the price-demand function.

In this research, for solving the problem of simultaneous pricing and planning, a joint production planning and pricing model in a multi-product and multi-period setting is proposed. The demand is considered to be price-sensitive and uncertain, while only a few price-demand estimations are available for each product in each period. For each price it is possible to determine the minimum and maximum demand occurring. In order to immunize the solution against demand variations, a robust mathematical model is proposed. In section 5.2.1‎ , a brief introduction to robust optimization is given, and then in sections ‎5.2.2, 5.2.3‎ , and 5.2.4‎ , the mathematical model used in the pricing and planning module is explained.

5.2.1 Robust Optimization

A robust optimization problem is defined as follows. Considering the

optimization problem of the form { }, define as the set of uncertain parameters in row of the matrix . Each member of the th row of the matrix , namely

, where , can be modeled as a random variable ̃ belonging to [ ̂

̃ ̂ ]. can be defined as . Obviously, [ ]. ̂

The first formulation of robust linear optimization was introduced by Soyster

(1973), and is as follows.

∑

(1) ∑ ∑ ̂

In this formulation, all the uncertain parameters are set to their worst case value.

Although this type of modeling obtains a good solution for all the realizations of uncertain data, the value of the objective function can be significantly far from the original optimization problem. To overcome the problem of the output being too conservative in Soyster’s formulation, another method was introduced by Ben-Tal and

Nemirovski (1998, 1999, 2000). However, in their formulation, potential computational tractability was a problem. To overcome the problem of the non-linearity and conservatism of the methods proposed Soyster and Ben-Tal and Nemirovski, Bertismas and Sim (2003, 2004) reformulated the model (1) in the following format.

∑

∑ ∑

(2)

Where is the maximum number of uncertain parameters in constraint , and and are the dual auxiliary variables which are used to guarantee the linearity of the model. Model (2) is a generalized form of model (1). In fact, if , models (2), (1)

∑ will be equal. Please note that | | .

According to Bertismas and Sim (2004), it is unlikely that all the have the worst possible value at the same time, and hence it seems more realistic to define a maximum number of uncertain parameters that may have the worst case value. demonstrates the protection level against the worst-case realization of uncertain parameters.

With this brief introduction into robust optimization, in the next section a mathematical model for simultaneous pricing and planning will be introduced, and in later sections a robust counterpart for it will be proposed.

5.2.2 Non-linear Model

The notation used in this research is as follows.

Parameters:

Holding cost of product per period

Production cost of product per unit

Lost sale cost of product per unit

th possible price of product in period 77

Demand of product in period when th price is chosen

Maximum production capacity for product in period

Budget in period

Variables:

1 if for th product in period , th price is chosen, and 0

otherwise

Sales of product in period

Inventory of product in period

Production of product in period

Let products in periods of time with possible prices in each period be produced. The proposed model for pricing and planning will be as follows.

∑ ∑ ∑ ∑ ∑

(3)

∑ ∑ ∑ ∑ ∑

(4)

∑ (5)

∑ (6)

∑ (7)

(8)

(9)

{ } (10)

The objective function maximizes profit by subtracting the inventory, production, and lost sale cost from sales. Constraint (4) is the inventory balance between inventory level, production, and sales. Constraint (5) guarantees that only one price for a product in each time period is chosen. Constraint (6) limits the maximum sales amount to demand, while constraint (7) assures the production budget does not exceed the maximum in each time period. Constraint (8) sets an upper bound for each product in each time period, and finally, constraint (9) bounds the production, sales, and inventory to positive integer numbers.

5.2.3 Linear Model

In problem (Q1), the demand is considered to have deterministic values for each possible price. However, it would be more realistic if the demand was considered to be a random variable belonging to an interval. To reformulate the (Q1) with demand uncertainties, the format of model (2) will be followed. However, since (Q1) is nonlinear, 79 one needs to linearize it before proceeding to propose the robust counterpart. Model (Q1) can be reformulated as a deterministic linear programming as follows.

∑ ∑ ∑ ∑ ∑

∑ ∑ (11)

{∑ ∑ ∑ ∑ ∑ ∑ }

(12)

(13)

∑ (14)

∑ (15)

∑ (16)

(17)

(18)

(19)

(20) 80

{ } (21)

(22)

in which and is a very large positive integer. Note that adding constraints (17-19) and introducing the new decision variable convert (Q1) into a linear problem (Q2).

5.2.4 Robust Model

As it is shown in Q2, the uncertain demand ( ̃ ) appears in the objective function coefficients and constraint coefficient as well. In order to simplify modeling the robust

counterpart of Q2, it is possible to substitute ∑ ∑ ∑ in the objective

function and add ∑ ∑ ∑ to the model as constraint.

In order to write the robust counterpart corresponding to the constraints involving uncertain parameters, first the protection function needs to be written, then the robust counterpart of Q2 can be concluded from the latter functions. Thus, model (24) is the

mentioned protection function where is the set of that ̂ (

{ | ̂ }), and is the budget uncertainty.

̂ ∑

∑

Moreover, the protection function corresponds to constraint (15) for a given and

is defined in model below where is the set of , that are subject to

uncertainty, and is the budget of uncertainty corresponds to constraint (15).

̂ ∑

∑

The robust counterpart of the problem (Q2) can be written as follows.

∑ ∑ ∑ ∑ ∑ ∑ ∑

(23)

∑ ∑ ∑

(24)

(25)

∑ (26)

∑ (27)

̅̅̅̅̅ ∑ ∑ ∑ ∑ ̅ (28)

̂ ̅ (29)

̅ ∑ ( ) ∑ (30)

̂ (31)

(32)

(33)

(34)

{ } (35)

(36)

̅ (37)

where , ̅ , , and are dual variables defined for the abovementioned protection functions. It is important to note that in the abovementioned model, there is uncertain demand appearing in two different constraints with two budget on uncertainties, and

that both of them are related to the number of uncertain demand to their corresponding constraints. Thus, there is a linear dependency between these two budget

of uncertainties, i.e., it is ∑ ∑ .

5.2.5 Solution Methods

For solving the proposed robust optimization problem, two methods are used in this research. The first method is using CPLEX Optimization Studio 12.3, which applies an exact method. Although this method gives an exact solution, for large instances it may take a very long time to find the optimum solution. The second solution method used is 83 unconscious search (US). US is a multi-start, memory-based metaheuristic that mimics the process of psychoanalytic psychotherapy. In the next two sections, solution methods will be explained in more detail.

5.2.5.1 Exact Method

The exact method used for solving the problem of simultaneous pricing and planning is using CPLEX Optimization Studio 12.3. The CPLEX code used in the pricing and planning module can be found in appendix A. Although the CPLEX yields the exact solution for this problem, but as the dimension grows, it becomes more and more time consuming to solve it by using CPLEX. Thus, it may not be the best method for real life problems. For this reason, an unconscious search algorithm is proposed for solving this problem.

5.2.5.2 Unconscious Search

Unconscious search is a metaheuristic algorithm. “Metaheuristics, in their original definition, are solution methods that orchestrate an interaction between local improvement procedures and higher level strategies to create a process capable of escaping from local optima and performing a robust search of a solution space” (Fred

Glover & Kochenberger, 2003). This approach in metaheuristics consists of transcribing the tendency in a natural phenomenon towards improvement in mathematical symbols and codes, as well as reducing the problem-solving operations into an algorithm that consistently traces the dynamics of that metaphorically deployed phenomenon. Some of the most well-known metaheuristics include Genetic Algorithm (Goldberg, 1989;

Holland, 1975), Simulated Annealing (Kirkpatrick, Gelatt, & Vecchi, 1983), Tabu Search 84

(F. Glover, 1989, 1990), Ant Colony (Dorigo, Maniezzo, & Colorni, 1996), and Particle

Swarm Optimization (Kennedy & Eberhart, 1995).

Since the original conceptualization that led to the development of metaheuristics and the inspired deployment of the probabilistic process entailed in “Survival of the

Fittest” as proposed by the Darwinian Theory of Evolution, further research has led to analogies with systems in new domains. The common thread running through all these is the set of rules by which the state of the domain undergoes a shift towards improvement.

Among these, the most unexplored areas are by far psychology and psychoanalysis (F.

Glover, 2007). Possessed of an integrated and united set of rules--which together improve the mental state of a patient-- psychoanalysis appears to offer a very promising metaphor in the area of optimization research. The unconscious search (US) metaheuristic, a method based on the analogy between concepts used in the psychoanalytic psychotherapy procedure and those in optimization problems, is used for solving simultaneous pricing and planning in this research.

Unconscious search is a multi-start, memory-based metaheuristic that mimics the process of psychoanalytic psychotherapy proposed by Sigmund Freud, where the therapist tries to find the root cause of a patient’s mental disorder in his/her unconscious

(Freud, 1913, 1975a, 1975b, 1993a, 1993b). In psychoanalysis, it is assumed that the cause of a mental disorder is lodged in the unconscious mind of the patient, and if the patient can remember that – i.e. make it conscious – his/her mental disorder will be resolved. However, the unconscious thoughts resist being revealed, and it is the job of the psychoanalyst to help the patient gain access to them by helping him/her overcome the 85 resistances. The most common patterns of resistance encountered during psychoanalysis are “displacement” and “condensation”. Displacement is the diversion of attention through substituting a signifier in a patient’s talk with another one that hides the unconscious better. Condensation is a type of resistance in which two or more signifiers in a patient’s talk are “condensed” into one symbol in order to hide the unconscious contents. In order to overcome the displacement and condensation resistances, the psychoanalyst tries to guide the patient what to start talking about and in which direction he/she should continue his/her talk. In other words, the psychoanalyst shows the patient the path to his/her unconscious based on their observations so far, and the patient tries to search more in depth on the path shown to him by the psychoanalyst.

Similarly, in an optimization problem the optimal answer is not already known, and in order to reach the optimum, one needs to overcome the resistances of the search space, which are in the form of local optimums. For this purpose, it is very important to know where to start and in which direction to move.

Unconscious search uses the same principle for finding the optimum solution. In each step, US maintains a list of the best found solutions and tries to find a good starting point and direction for searching by using these solutions and memorizing the starting points and directions that led to finding these solutions. For this purpose, US uses two types of memory, namely “displacement” and “condensational” memories. Displacement memory memorizes the most promising areas for the starting point, while condensational memory memorizes the most promising directions for searching. Whenever US finds a good solution, it tries to improve it further by using a local search. 86

US has been used in various optimization problems so far (Amin-Naseri,

Ardjmand, & Weckman, 2013; Ardjmand & Amin-Naseri, 2012; Ardjmand, Park,

Weckman, & Amin-Naseri, 2014). To explain the details of US, consider the following optimization problem1.

The objective function may be linear or nonlinear. Functions and

are constraints of vector , where is the set of decision variables, and condition

restricts the components of to a range of values. For solving optimization problem , initially, a set of feasible solutions ( ) is generated.

is the size of the measurement matrix in which the sorted set of the best feasible solutions, i.e. those nearest to the optimum solution that are visited during the search process, are held. can be defined as follows:

{ ( ) ( ) } (38)

The solutions kept in are used to measure the resistance, and are ranked by means of a “translation function” according to the value of said resistance. The translation function maps the value of the objective function of any solution (i.e. a solution that belongs to ) into a range for where .

1 - Note that the notations used for explaining unconscious search is independent of the rest of this research and belongs only in this section. 87

Any solution that does not belong to and an objective function that is greater in value than the worst solution within is assigned a scalar penalty value .

The translation function is defined as follows:

( ( )) (39) ( ( ))

In (39) above, is a sigmoid function and is used to calculate the proximity of solutions in to the optimum solution (i.e. “unconscious” Λ { }, see

Figure 1). and are the parameters of and are calculated in every iteration in the course of this search.

Figure 13 is a plot of the translation function against the values of the objective function for the members of the measurement matrix. As can be seen from the graph, the best member of the measurement matrix is assigned the value , while the worst member is assigned the value by the translation function. For any solution that lies outside the measurement matrix for which the objective function is greater in value than the worst solution within , there is a penalty value assigned to that

solution. Note that in minimization problems, ( ) and

( ) . Conversely, in maximization problems we have

( ) and ( ) .

Figure 13. Translation function and measurement matrix

Evaluating the resistance level in solutions is performed by means of the

translation function and by the displacement and condensational memories. measures the quality of the solutions, while the displacement and condensational memories memorize the resistance patterns in the solutions. The displacement memory, shown by , memorizes the displacement pattern of resistance in the solutions, i.e. dividing the possible range – considering that – of every solution component into

equal parts. It then assigns the output of ( ) to the corresponding part. In other words, determines how much resistance will occur if a specified range of is assigned to solution component .

can be defined as follows:

{( ) } (40)

in which,

{ } (41)

{ } (42)

and is the number of decision variables. and are defined as follows:

(∑ ( ( ))

(43)

)

∑ for solutions with an objective function

greater than the worst solution in (44)

in which { } is the Memory Size that shows the last performed iterations of algorithm that are memorized. represents the jth subinterval of . As we increase the value of the parameter , the effect of those lower quality solutions encountered in the previous iterations on determining the search path becomes more apparent. Increasing

has the advantage that it causes diversification to increase; on the downside, it could lengthen the time spent on searching. (To make this point clearer, compare it with the metaphor of psychoanalysis: as the psychoanalyst gets closer to the unconscious, associations made by the subject become more representative of the contents of the 90 unconscious, and hence are more important to the psychoanalyst.) is the worst solution in , and is the value of the th decision variable in solution .

By means of the displacement memory , a new solution can be constructed. This solution is denoted by . The th solution component will be assigned to one of the possible ranges in solution space, with a probability defined as follows:

( ) { } (45)

∑ ( )

in which is the probability function and is a predefined constant. When the solution component is assigned to , it will choose a number in at random. The

larger the value of , the more the probability of ; the larger the value of , the less the probability of .

Once a displacement-free solution (DFS) has been reached, the condensational memory is used to eliminate the condensational resistance pattern. Displacement memory is used for constructing a new displacement-free solution (DFS), while condensational memory is used to improve the solution constructed with the help of , making it a condensation-free solution (CFS).

Condensational memory is defined as follows:

{ } (46)

in which,

{ } (47)

{ } (48)

where,

∑ ( ( ))

is increased with respect to its previous value (49)

in the first iteration of a local search

∑ for solutions with an objective function

greater than the worst solution in th (50) decision variable is increased with respect to its previous

value in the first iteration of a local search

∑ ( ( ))

is decreased with respect to its previous value (51)

in the first iteration of a local search

∑ for solutions with an objective function (52) greater than the worst solution in th 92

decision variable is decreased with respect to its previous

value in the first iteration of a local search

Note that, since in the beginning of the first iteration of US, we do not perform a local search, we do not have any information with which to update ; thus, equations

9~15 are applied from the second iteration onwards.

Once is constructed, determines whether is to be decreased or

increased by calculating two values and and generating a random

number 휓 in the range . If 휓 , the value of will be increased by as

much as a predefined number δ { }; otherwise, the value of will be decreased by the same amount δ. Decreasing or increasing the value of will be repeated until the limits of are reached, as long as the solution still remains feasible.

Having constructed , the first solution in an iteration is known as the “mother solution”. By using memory , solutions , , … are generated from . Solution is the DFS, while solutions , , … are CFSs derived from the mother solution . The

best solution among , , , …, called ,will be the starting point in the local search.

Memories and help to appoint the region where the mother solution should be located and the direction along which the mother solution is to be moved, by increments of δ, in order for the solutions , , … to be generated. The functions of these two memories for the situation where there are two decision variables and are shown in Figure 14.

Figure 14. Functions of 횷and 횷 for the situation where there are two decision variables, and

After obtaining the solution , a local search is conducted with as the starting point. If the result of the search is , it is obvious that . In the process of reaching , more resistance patterns are revealed, and and are updated by the use of

. Notice that will be updated only if the objective function value of is better than the objective function value of , in which case will be updated so that the following inequality holds:

(53)

in which and are the members of before is augmented. In order for the above inequality to always hold, should remain sorted through every update. If

is changed, the function must be corrected to match the new , i.e. the coefficients and must be adjusted. Denoting the new coefficients by and , as well as the best and the worst solutions in by and , we will have: 94

( ( )) (54)

( ) ( ( )) (55)

US is a multi-start metaheuristic which contains three main phases:

1- Construction

2- Construction review

3- Local search

The first phase is equivalent to constructing a displacement-free, or “mother”, solution. The second phase is equivalent to constructing condensation-free solutions derived from the mother solution in Phase 1. The third phase corresponds to the recognition of the resistance patterns through an exploration of the search space.

5.2.5.3 Applying an Unconscious Search to Pricing and Planning Module

To apply a search to simultaneous planning and pricing, the steps involved in an unconscious search will be followed. After the initialization of the algorithm, the first step is to construct a solution based upon displacement memory. For this purpose, a price for each product in each period will be determined according to the scores in displacement memory. Note that determining the price is building a partial solution, because the production plan and sales amount in each period still need to be determined.

To complete the solution, a Simplex algorithm (Dantzig, 1998) will be applied. The reason for using a Simplex algorithm is that, after obtaining the prices and replacing them 95 in the model, no binary decision variable remains in the model, and it thus turns into a linear model without any binary variables. Solving this linear model with a Simplex model is very easy and possible in polynomial time. The Simplex C++ code used can be found in appendix B (Moreau, 2009).

After the partial solution generated by an unconscious search is completed by using a Simplex algorithm, the second step of US--construction review--is started. In this step, the prices of products in each period are increased or decreased based upon the condensational memory. After each change in price, a Simplex algorithm is used to complete the solution. Finally, after the construction review step, a local search is conducted to improve the solutions. In a local search, a random price for a product in a random time period is picked and changed. If the results improve, the change will be accepted; otherwise, it will be rejected, and another product or period will be picked. This procedure continues until no further improvement is possible. Figure 15 shows the flow chart of applying an unconscious search to the problem of simultaneous pricing and planning.

Figure 15. Flow chart of applying unconscious search to pricing and planning module

5.2.5.4 Verification of Unconscious Search Results

To verify and evaluate the efficiency of a proposed unconscious search, a set of six test problems are generated and the results of US on these test problems are compared to the results obtained by using CPLEX. For each product in each period, a random number between 200 to 300 is generated as nominal demand, and it is assumed that all the demands can change up to 25%. Finished cost, inventory cost, and lost sale cost are generated randomly from the interval [ ]. Three choices of prices are considered for each product in each period, which are 120, 130 and 150. Space occupied for each 97 product is considered to be 2, while the warehouse and budget capacity for each period are fixed at 5000 and 50000, respectively. The maximum production number for each product in each period is set to 700. Table 10 lists the six test problems’ specifications, including the number of periods and products in each.

Table 10: Test problems’ specifications used for evaluation of unconscious search Test Problem No. of Periods No. of Products

1 1 4

2 1 4

3 2 5

4 2 5

5 4 10

6 4 10

Table 11 lists the results of the exact and US algorithms applied to the six randomly generated test problems. Each test problem is solved by US ten times, and the best and worst results obtained are reported. As it can be observed, US has been able to find the optimum solution in a very short time compared to the exact method. The time gap between the two algorithms is even more evident as the dimension of the problem increases. The results obtained show the efficiency and quality of US for solving joint pricing and planning problems. Note that in test problems 5 and 6, the value of the objective function is negative, due to budget constraints and the high number of lost sales. 98

Table 11: Solution quality and run time of exact and US algorithms for six artificially generated test problems; for each instance, US has run 10 times

Test Exact Method Unconscious Search

Problems Exact solution Time (s) Best Solution Worst Solution Time (s)

1 37005 2.94 37005 37005 0

2 49540 1.95 49540 49540 0

3 31364 2.43 31364 31364 0

4 95980 2.43 95980 95980 0

5 -169216 15.85 -169216 -169216 0

6 -92622 19.67 -92622 -92622 0

5.3 Design and Outputs of Pricing and Planning Module

The pricing and planning module has two outputs. The first output is the price for each product in each period, and the second output is the production and sales plan for each product and period. Figure 16 shows a prototype of a pricing and planning interface, where the specifications of each product and period, as well as the constraints, can be adjusted. The inputs from finance and cost estimation modules will be loaded into the interface automatically.

Figure 16. A prototype of pricing and planning interface

Figure 17 depicts the inputs, processes, and outputs of the pricing and planning module.

Figure 17. Inputs, processes and outputs of the pricing and planning module

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6 SCHEDULING MODULE

The third module of proposed decision support system is scheduling. A scheduling module, having a production and sales plan as an input, schedules a plan calculated by a pricing and planning module in each time period. For this purpose, in addition to scheduling the products on stations, it is necessary to control the progress of jobs at hand. Hence, there are two main processes in a scheduling module. The first process is scheduling the tasks, and the second one is controlling the progress of scheduling and to make corrections if necessary. In this chapter, the inputs, processes, and outputs of a scheduling module are introduced.

6.1 Inputs

The first set of inputs to a scheduling module, which is the production plan, comes from the pricing and planning module. In addition to a production plan, the available times and production specifications--such as flow process charts, machines, and the skill level of operators--are the other inputs of a scheduling module. These inputs will be discussed in detail in the following sections.

6.1.1 Inputs from Pricing and Planning Module

The first input of a scheduling module is the production plan generated in a pricing and planning module. A production plan consists of a product, the number of its production in a time period, and the length of the period. As an example, if a pricing and planning module has determined 200 as the number to produce in period , then the scheduling module will receive this input as a task that needs to be scheduled, while its release time and deadline are the beginning and ending of period , respectively. Hence, 101 the output of the pricing and planning module will be introduced to the scheduling module in the form of jobs. Each job has several attributes. These attributes include the product, number of production, release time, deadline, priority, and the delay between different stages of production. The delay between production stages is the time that should pass until an activity can be started after all its predecessors have been scheduled.

6.1.2 Timeline and Working Hours

In order to schedule the tasks, it is necessary to know the working and non- working hours, break times, and number of working shifts for each day. All these specifications of a timeline will be called a work profile. A work profile has various attributes by which time colander and available times can be defined. An example of a database designed for recording profiles can be found in appendix C. Different working profiles can be defined for the system and used according to need. In scheduling, only allowed times obtained from work profiles will be used for calculations. Note that, although the constraint imposed by work profiles may increase the complexity of scheduling dramatically, but it is necessary to consider all these constraints in order to have a realistic scheduling setting.

6.1.3 Machines

Machines are the processing units of scheduling problems by which a product is processed. In this research, any processing tool is considered to be a machine. A machine’s performance is an indicator of how reliable that machine is in finishing a job on time. The performance of a machine in this research is evaluated by using “Overall

Equipment Effectiveness” (OEE). OEE is the lean time that a machine properly works. In 102 calculating the OEE, only the time that a machine is working without being interrupted or producing defective products is considered. Figure 18 indicates how the OEE can be calculated after subtracting from the scheduled time the repair and inefficient times plus the times a machine is producing a defective product. Repair time is the time that a machine needs immediate attention due to an unexpected stoppage or interruption in the production process, while inefficient time is the time that a machine loses due to variations in standard cycle times.

OEE is a very comprehensive measurement criterion in terms of evaluating the efficiency of production lines (Dal, Tugwell, & Greatbanks, 2000; Godfrey, 2002;

Muchiri & Pintelon, 2008). In this research, OEE will be used to determine and modify the total numbers of production needed on a machine. As an instance, if 200 units of a product is to be produced on a machine and the machine’s OEE is 0.9, it makes more

sense to schedule units for that machine. The extra 22 units are due to the various inefficiencies that the machine has.

Figure 18. The lean time remains after subtracting the repair and inefficient times plus the amount of time a machine is producing defective products

103

6.1.4 Maintenance

Having the machines as inputs, it is necessary to know the maintenance time associate with each of them. Maintenance is important because it can make a machine unavailable for some time intervals, and hence affect the scheduling. A machine may have various types of maintenance for each of its parts. To track the maintenance times, all parts of a machine need to be defined and their maintenance time recorded. An instance of a database designed for tracking the maintenance can be found in appendix D.

6.1.5 Stations

A station involves set machines and operators that altogether work towards assembling or producing a part or a stage of a product in its production path. Note that a station can have one or several machines as its content. Definition of a station is necessary because sometimes it is more convenient to define the stages of production for a product in the form of stations. Note that each product can have different activities performed on each station.

6.1.6 Setup Times

Each product may have different warm up or setup times on different stations.

These times can also be dependent on the product that it had just been producing. The setup times of products on each station is defined in the form a matrix in which each component corresponding to row and column shows the setup time for changing from product to product . To formulate the scheduling module more realistically, the setup time of each product is considered to have two parts, variant and invariant. The variant 104 part can be different depending upon the prior product, while the invariant part is fixed for each product.

6.1.7 Operators and Skill Levels

Operators and their relative skill levels for producing different products are the inputs of a scheduling module. For assessing the skill level of each operator in association with the various activities involved in producing a product, a visual ILUO method is used. In an ILUO method, the skill level of each operator is categorized in four categories of I, L, U, and O, in which I is the least and O is the most skilled level

(Graham & Clare, 2007; Handyside, 1997). Note that in an ILUO method the skill level has different parameters, such as meeting quantity, quality, and safety standards. In the proposed decision support system, the skill level of each operator is determined by the user.

6.1.8 Operation Chart

An operation chart (OC) is an essential input for a scheduling module. In an OC, the production stages of a product, along with the various activities involved and cycle times, are included. In flow shop and job shop problems, a product is supposed to go through several stages in a linear fashion to yield a final product. However, in reality, in producing one unit it is necessary to have a network of stages and stations that altogether form an OC for a product. In this regard, an OC is similar to the networks used in project management. Figure 19 depicts a prototype of an OC for a product consisting of six stages/stations. Each rectangular shape shows a stage or station of production. 105

Figure 19. A prototype of an operation chart consisting of six stages

6.2 Processes

A scheduling module has two main processes. The first process is scheduling the jobs. A job can be the output of a pricing and planning module, or a single job defined separately by a user. It is even possible to consider a part of a product’s operation chart as a job and schedule it. In total, any set of tasks that needs to be scheduled can be considered as a job. The only constraint is that these tasks need to be related to production. For instance, scheduling module cannot schedule a maintenance task.

The second process of a scheduling module is controlling how the progress of a schedule is monitored and, if there is any deviation, how it will be reported to the user.

The control process helps to correct the schedule if necessary, and can also be a great experience accumulation source by finding possible failure modes of a production line. In the following sections, scheduling and control processes are explained in more detail. 106

6.2.1 Scheduling

Generally speaking, the goal of scheduling is to arrange and sequence the jobs on different machines in order to optimize the resources’ consumption (Pinedo, 2012). The setting considered for a scheduling module of the proposed decision support system is a general setting in which most of the scheduling problem attributes are present.

In literature, among the standard scheduling problems, flexible job shop problems are the most complex ones. Flexible job shop problems are a generalization of job shop problems in which each an operation can be processed by a set of allowed machines.

However, the environment set for a scheduling module is more general compared to a flexible job shop. In a flexible job shop, each job consists of a chain of operations in which each operation can be handled on several parallel machines. In the proposed decision support system, each job has several operations arranged in a network instead of a chain. Hence, the problem is a combination of project and flexible job shop scheduling.

In addition to the scheduling environment, other attributes of the proposed scheduling module are also considered to be general as much as possible. The release dates of jobs are considered to be non-zero, which can increase the complexity of the problem. Setup times are sequence-dependent, and hence, each sequence of the jobs may yield a different setup time. Jobs can be broken down into two or more parts. Some parts of the timeline are blocked, and hence it is not possible to use them in scheduling. A good example of blocked times are the holidays, where no job should be scheduled.

The objective of scheduling problems is considered to be the minimization of weighted tardiness, which is one of the most complex objectives in scheduling literature 107

(Pinedo, 2012). This objective is necessary because, after defining the production plan in a pricing and planning module, the scheduling module has to guarantee that planning output is feasible in the designated time window. The objective function needs to be weighted because the system user may set different weights for jobs due to their importance for customers or any other requirements necessary.

In addition, as mentioned in section ‎6.1.3, each machine has an effectiveness measured by the OEE. The OEE of the machines can affect the scheduling problem.

Hence, it is necessary to take the OEE into consideration. For this purpose, the completion time of each task or operation on a machine cannot be deterministic, and needs to be treated as a stochastic parameter which is directly related to the OEE. As an example, if the completion time of a task on a machine is 1 hour in an ideal situation and the machine’s OEE is 50%, then the processing time needs to be considered a random variable between 1 to 1.5 hours.

Handling the scheduling problem in a general setting is a very computationally expensive task, and in a dynamic environment such as a production line, needs to be done in the shortest possible amount of time. In order to address this problem efficiently, it will be divided into two parts and treated separately. At the end, the two parts will be combined again to form a complete solution. The reason for this division is the high complexity of the proposed scheduling problem and the fact that there is not any unique procedure for dealing with the problem at hand.

To propose a heuristic algorithm for the proposed scheduling problem, it will be divided into two parts; dispatching and simulation. In the dispatching phase, the sequence 108 of jobs will be decided. Note that the constraints--such as release tim-- are not considered in this step. The question answered in this phase is of which job should enter the production line first. Also, it is assumed that when a job is entered the line it can consume all the resources necessary without taking the requirements of next job into consideration.

In this regard, the problem will be reduced to a simple travelling salesman problem

(TSP), which can be solved by a good heuristic efficiently. The heuristic used in this research is the variable neighborhood search (VNS).

In the second phase, after determining the sequence of the jobs, the jobs need to be scheduled separately. For this purpose, each job needs to be scheduled individually as well. Since each job is a project with probabilistic task durations, the problem of scheduling a single job is also a complex problem. For solving this problem, a Monte

Carlo simulation method is used, in which different values are assigned to task durations based on the OEE of the machines.

Figure 20 shows the general framework of the heuristic used in scheduling modules for sequencing the jobs. The process of scheduling a single job and the sequence of the jobs will be explained in the following sections.

109

Figure 20. General framework of the heuristic used in a scheduling module

6.2.1.1 Scheduling One Job

For scheduling a sequence of jobs in the proposed decision support system, it is necessary to schedule each one of them separately. Each job in the system is presented as a network of tasks that are related to each other by precedence constraints. From this perspective, scheduling a job is very similar to assigning resources in project management problems. For a project to be done on time, it is necessary to control the critical path’s time and resources. For a product that is considering the operations chart, the critical path is the set of all the activities that together form the longest path from the beginning to the end of production. Figure 21 depicts a hypothetical operations chart for a 110 product and its corresponding critical path in red. Each circle shows a station that the product needs to meet before completion. Although it is necessary to perform all the tasks to have the product ready, in order to guarantee the timely finish of the product, all the tasks on the critical path need to be done on time. The red path in Figure 21 is the longest route from the first to the last station in terms of processing time. In this example, to finish the project on time, it is necessary to control the times for the tasks 1, 3, 5, and 7.

Figure 21. A product’s operation chart and its critical path

Using the logic of critical path method, it is possible to schedule a job by assigning the necessary resources to its critical path first. However, due to the stochastic nature of the processing times, a critical path may not always stay critical. Depending on the task durations of a product’s operations chart, there may be different critical paths. To find different possible critical paths, a Monte Carlo simulation is performed. In the simulation, each time a processing time is assigned to tasks, based upon the average processing time and OEE of the machine used. Then, the critical path is determined.

Having different possible durations, a task may be part of a potential critical path. The 111 number of times a task appears on all potential critical paths is the indicator of how important that task is for finishing the job on time. Hence, the tasks with a higher number of appearances on critical paths will be given priority for assigning the necessary resources for production. In addition to being on the critical path, precedence constraints are another factor that should be taken into consideration for scheduling a task of a job.

After determining the tasks of a job with a higher priority given to assigning the resources, they need to be scheduled in a manner that does not conflict with blocked parts of the timeline. In addition, setup times need to be considered. For instance, consider a task that needs to be scheduled on a station with two time blocks that can’t be used, due to maintenance and another task that has occupied a part of the station timeline. Figure 22 depicts this situation.

Figure 22. a) original timeline b) timeline after scheduling task A

In part a) of Figure 22, the original timeline is shown, in which two time blocks are reserved for maintenance (black blocks) and task B is also scheduled (blue block).

Hence, the time block of task B cannot change. It is assumed that at the beginning of the timeline, the station is ready for production and the only time needed to start task A is a warm up time (striped block). Thus, three warm up periods are needed because each time task A is interrupted, it needs another warm up period to start again. In addition, when 112 one schedules task A after task B, a setup time is necessary (grey block). A good method for scheduling jobs in a real setting needs to implement all these constraints after determining the priority of tasks.

Figure 23 shows the flowchart of scheduling a single job. First, all the specifications of the job are read from the database. Then, using the OEE of the machines needed for the job and the average task’s durations, a Monte Carlo simulation is conducted to determine the possible critical paths. Based on the number of times that a task appears on the critical paths, the tasks are then prioritized. At the end, considering the existing constraints on the schedule and the precedency, all the tasks are scheduled.

This procedure continues until the whole job is scheduled.

113

Figure 23. Flowchart of scheduling a single job

6.2.1.2 Optimizing Dispatching Rule Using Variable Neighborhood Search

After introducing the procedure for scheduling a single job, it is necessary to implement all of the jobs in order to minimize the total weighted tardiness. The problem of determining an optimum sequence for dispatching the jobs into a production line can be interpreted as a traveling salesman problem (TSP). In TSP, the objective is to find a

Hamiltonian path in a directed or undirected graph so that the sum of weights of the vertices on the path is minimized. Likewise, in finding the best sequence of jobs, the objective is to find an ordered set of the jobs that include all of the jobs and, if 114 implemented in that order, minimize the total tardiness. For solving the proposed TSP, a variable neighborhood search (VNS) is applied.

VNS is a metaheuristic which operates based upon changing the neighborhood systematically (Hansen & Mladenović, 2003; Mladenović & Hansen, 1997). To explain

VNS, consider an optimization problem of the form { }. Let us define as the set of neighborhood structures. Hence for a solution , there are solutions that are its neighbor and can be reached by the th neighborhood structure. In basic VNS, first an initial solution s chosen. Then, having

, the neighbors of the generated solution are examined until a local optimum is reached. In the next step, will be increased by one, and the same procedure is repeated until a local optimum is reached. This procedure continues until all the predefined neighbors are examined.

The same procedure can be applied to a sequence of jobs to find a good dispatching order. For this purpose, four neighborhood structures are defined. The first neighborhood structure can be explored by swapping two jobs in a sequence. The second neighborhood structure can be navigated by examining three consecutive jobs in a sequence and finding the best order for them. Using the same logic, the third and fourth neighborhood structures are obtained by examining all permutations of four and five consecutive jobs in a sequence. After reaching a local optimum at the end of each neighborhood structure search, the next neighborhood structure is initiated.

Figure 24 shows the flowchart of applying VNS to finding the best sequence of the jobs for scheduling. First, the set of neighborhood structures are defined and a random 115 sequence of the jobs is generated. Then, starting from the first neighborhood structure, a random job in the sequence of jobs is picked, and all the permutations of to

in the sequence in which is the index of neighborhood are evaluated. Among all the permutations, the best one is picked and the sequence is updated accordingly. After finding the local optimum using a neighborhood structure, the next structure will then be initiated. This process continues until all the neighborhood structures are examined and the termination criteria is met. Note that in Figure 24 , for evaluating each permutation, each job in the sequence needs to be scheduled using the method introduced in section 6.2.1.1‎ .

Figure 24. VNS algorithm for finding the best sequence of jobs for scheduling 116

6.2.2 Control

The second process of scheduling model is “control”. This process is necessary to make sure that the schedule is on time, and thus supports the objectives of the pricing and planning module. The control process has two main parts. In the first part, all the production interruption causes are recorded, while in the second phase the action plans taken to remove these causes--along with previous knowledge in the case of the same interruption--are recorded. To have all this data stored, it is necessary to have a database capable of storing the data in a format that can be easily accessed.

Production interruptions can be categorized into two parts. The first group of interruptions are those related to quality issues and production defects. For these interruptions to be recorded, it is necessary to define the possible defect types for each product and then, whenever an interruption of this type occurs, the reason and the action taken are to be stored as possible action plans for future reference.

The method used for identifying and keeping track of problems and their causes is fishbone diagram. A fishbone diagram helps to find the root cause of a problem without using numerical and statistical approaches (Bicheno, 1998; Goetsch & Davis, 1994;

Psychogios & Priporas, 2007). In a fishbone diagram, the root cause of each problem is considered to belong to one of the following categories: method, machine, manpower, material, measurement, or environment.

In addition to quality problems, other types of production interruptions also need to be monitored and their related data recorded in the database. These interruptions are 117 those related to issues such as logistics, production processes, operators, and energy resources.

Figure 25 depicts the domain model of a control process in terms of the scheduling module. Rectangular shapes are the entities that need to be recorded and stored in the database. Green parts are related to quality issues, while blue parts are related to other interruption types. Yellow parts are used for both quality and non-quality problems. Arrows show the relation of entities to each other. For instance, a product is connected to production-defect by an arrow, which means that each product can have several defects related to it. In the same manner, defects are connected to product-defect, which means that each defect type can affect several products.

One of the entities introduced in Figure 25 is “process”. A process is any kind of activity that is taking place in production, and may include operators and machines. A process is a part of a working station in a production line. To explain the concept of process, consider a production line that produces raincoats. There is a station in the production line dedicated to producing sleeves, and for sewing a sleeve, two sewing machines are needed. One sewing machine is used for sewing the front and the other for the back of the sleeve. In this case, sewing the front of the sleeve is a process that needs a machine and an operator.

Using the process as a basis for monitoring the production line, it is possible to control the line to keep the schedule on time. For monitoring the production line, two indicators can be used--namely, overall equipment effectiveness (OEE) and parts per million (PPM). OEE was discussed in detail in section ‎6.1.3. PPM is the number of 118 defective products in a million. The control process of a scheduling module helps to monitor these two indicators and take quick action when they are not in a defined range.

Both of these indicators can be calculated by the database structure depicted in Figure 25.

Figure 25. Schematic domain model of the database for a control process in terms of the scheduling module

6.3 Design and Outputs of Scheduling Module

As discussed in previous sections, a scheduling module has several inputs, processes, and outputs. Figure 26 shows the different parts of scheduling module, including the inputs, processes, and outputs. In the input part, the rectangular shape 119 shows a module of the decision support system which feeds the scheduling module automatically, while the other inputs are introduced into the system by a user.

The outputs of a scheduling module include a schedule, which will be used by an inventory module, and two indicators – i.e. OEE and PPM – for monitoring the performance of the system.

Figure 26. Inputs, processes and outputs of a scheduling module

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7 INVENTORY MANAGEMENT MODULE

The inventory management module is the last in a series of modules for the proposed decision support system that makes decisions based upon the outputs of the finance and cost estimation, pricing and planning, and scheduling modules. This module coordinates the inventory decisions in such a way as to guarantee the availability of necessary raw materials for supporting the scheduling module. Thus, the first assumption for an inventory management module is that no material shortage is allowed. Similar to other modules, inventory management has a set of inputs, processes, and outputs. In the remainder of this section, inputs, processes, and outputs of an inventory management module will be explained.

7.1 Inputs

The inputs to an inventory management module can be divided into two groups.

The first group is those that are originated from other modules, and hence are automatically generated. The second group is those that need to be defined by the user.

These inputs include a bill of material (BOM), as well as supplier and material specifications. Although the automated inputs from other modules are generated automatically, it is possible for them to be modified by the user as well. In the following sections, these inputs will be explained in detail.

7.1.1 Inputs from Scheduling Module

The first set of inputs to an inventory management module originate from the scheduling module. Following the decision made by the pricing and planning module, the scheduling module arranges a sequence of the jobs in a way so as to guarantee the 121 feasibility of the plan. For a schedule to hold and be performed, it is necessary to support it by the availability of necessary raw material at the proper time and in the proper amount. The inventory management module receives the schedule as an input and estimates the raw materials’ consumption based on it.

7.1.2 Inventory Holding Cost

Each raw material has a holding cost that is estimated by the finance and cost estimation module. In the same manner that the holding cost of products was computed by the finance and cost estimation module, it is possible to estimate the holding cost of raw materials. The holding cost of raw materials varies based on their characteristics such as purchase value, space occupation coefficient, and perishability.

7.1.3 Bill of Material (BOM)

To estimate the raw material consumption using a schedule of jobs, a bill of material (BOM) is used. BOM is the set of raw material and components as well as their needed amount for manufacturing a product. BOM is an input that needs to be defined by the user. It is possible to have several BOMs for a product. However, only one of them is considered to be active for planning purposes. The active BOM also needs to be defined by the user.

7.1.4 Suppliers and Material Specifications

In addition to a BOM for each product, the specifications of the needed materials and the set of suppliers that provide these materials need to be defined. These specifications include: the ordering cost of a raw material to each supplier; the purchasing price of a material from different suppliers; the minimum and maximum possible order 122 quantity for each raw material to each supplier; and the space occupation coefficient of materials.

7.2 Processes

The main process of an inventory management module is to determine which raw material--in what amount and to which supplier--should be ordered in order for there to be no interruption in the schedule while minimizing the purchasing, holding, and ordering costs. The method used for addressing this problem in this research is mathematical modeling. Note that this problem is defined in a deterministic setting. The reason is that the demand and a job’s processing time uncertainty is dealt with in the pricing as well as the planning and scheduling modules. Hence, the inventory management module just needs to support the strategy advised by the other two modules. In section ‎7.2.1, the mathematical model for an inventory management module is proposed, which is the basis of all decisions made in this module.

7.2.1 Mathematical Model

The following notation is used for modeling the inventory management problem.

Indices:

Material

Periods

Suppliers

Parameters:

Inventory holding cost of Material 123

Cost of ordering material from supplier

Demand of material in period

Purchasing price of material from supplier

Space occupation coefficient of material

Minimum ordering quantity of material to supplier

Maximum ordering quantity of material to supplier

A large number

Decision Variables:

Inventory level of material at the end of period

1 if material is ordered to supplier in period and 0 otherwise

Amount of material ordered to supplier in period

The mathematical model will be as follows:

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ (56)

S.t. (57)

∑ (58)

∑ (59)

(60) 124

(61)

(62)

{ } (63)

The objective function minimizes the costs of holding inventory, ordering, and purchasing. Note that, although shortage cost is a common assumption in inventory models, since the inventory management module has to support the scheduling module, it cannot have a shortage. Thus, the shortage cost is not considered for this model.

Constraint (58) is the inventory balance equation. Constraint (59) limits the inventory level to warehouse capacity. Constraint (60) limits the ordering quantity of each raw material to a minimum quantity. Constraint (61) makes the ordering quantity 0 if the respective supplier is not chosen for placing an order. Constraint (62) limits the ordering quantity to an upper bound, and constraints (63) are non-negativity and binary constraints.

7.2.2 Solution Methods

In order to solve the proposed mathematical model for the inventory management module, two methods will be used and compared against each other. The first method is the exact one in which CPLEX 12.3 is used. The second method is a hybrid of a tabu search metaheuristic and a Simplex algorithm. In the following sections these two methods will be explained in detail. 125

7.2.2.1 Exact Solution

To solve the proposed model in an exact way, CPLEX 12.3 is used. Although the

CPLEX obtains the global optimum, due to the large scale of the problem when there are many types of material or time periods, it becomes very time-consuming to apply CPLEX to the problem. Hence, it is not possible to use CPLEX in real life cases of the problem.

The CPLEX code of the problem can be found in Appendix E.

7.2.2.2 Hybrid Tabu Search and Simplex Algorithm

Tabu search (TS) is a metaheuristic, which is designed to overcome local search

(LS) methods in escaping local optimums (F. Glover, 1989, 1990, 1997, 2007). Search space and neighborhood structure are the two main concepts in TS. Search space is the set of all possible solutions which can be reached in the course of a search. Neighborhood structure is the type of local transformation that can be applied to a solution in order to reach a new solution in search space. It is possible to have various neighborhood structures in a problem.

In TS, while searching for the optimum solution, a tabu list is maintained. A tabu list is the set of recently performed transformations that, by being repeated, may cause the set to revisit prior solutions. A move can be tabu up to a certain number of iterations.

However, if a recently performed move can improve the solution considerably, it can be performed. The criteria by which a recently performed move can be repeated despite being in a tabu list is called the :aspiration criteria”. A tabu list is also known as short- term memory (Fred Glover & Kochenberger, 2003). 126

In addition to short-term memory, another type of memory--long-term memory-- is used in TS. Long-term memory memorizes the promising domains of search space, and helps to find a better starting point whenever the search is restarted.

A TS method will be used for solving the proposed inventory management model.

TS will be applied to the problem in order to determine if material needs to be ordered to supplier in period or not. Thus, TS will only determine the value of the binary variable . However, after deciding about the , the amount of material ordered also needs to be determined. Following the model, if the values for are known, the model will turn into a simple linear optimization problem that can be solved efficiently using a Simplex method. In fact, and will the output of the Simplex method.

Thus, a two-stage hybrid algorithm will be used for solving the proposed model in which, in the first stage, the values of are calculated using a TS algorithm. In the second stage, the values of are considered fixed, and a Simplex method will be applied to determine the values of and . The Simplex method used in the solution procedure is the same as the one used in section ‎5.2.5.3.

To show how the proposed algorithm can be applied to the problem, the following notation is used.

{ } Current solution

A part of the solution that shows the set of suppliers chosen

for providing materials in each period

A part of the solution that shows the amount of each 127

material ordered to each supplier for each period

A part of the solution that shows the inventory level of each

material in each period

{ } The best known solution

Objective function of

Neighborhood of

Neighborhood of which is not tabu or is allowed by ̃ aspiration criteria

Figure 27 depicts the flowchart of the proposed hybrid algorithm for solving the inventory management model.

Figure 27. Flowchart of the hybrid tabu search and Simplex algorithm applied to the inventory management problem

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7.2.2.3 Verification of Hybrid Algorithm

To verify the solutions obtained using the proposed hybrid algorithm 6 different test problems are generated. The specifications of the problems are listed in Table 12. For ordering cost, demand in each period, purchasing cost, space occupation coefficient, inventory cost and minimum and maximum number of supply units by a supplier a random number from the intervals [ ], [ ], [ ], [ ], [ ] and [ ] is generated respectively. In all instances, the warehouse capacity is considered to be 1000 units of space.

Table 12. Six randomly generated test problems for verifying the hybrid algorithm Problem No. of products No. of suppliers No. of periods

1 5 3 5

2 10 3 5

3 10 5 10

4 15 5 10

5 15 10 10

6 20 10 15

Table 13 lists the solution obtained and run time of exact and hybrid algorithms for 6 artificially generated test problems. For each instance, hybrid algorithm has run 10 times.

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Table 13. Solution quality and run time of exact and hybrid algorithms for six artificially generated test problems where for each instance the hybrid algorithm has run 10 times Test Exact Method Hybrid Algorithm

Problems Exact solution Time (s) Best Solution Worst Solution Time (s)

1 4221 2.44 4221 4221 0.00

2 5746 3.21 5746 5746 0.00

3 18574 3.43 18574 18574 1.12

4 27356 5.00 27356 27356 1.24

5 32115 4.49 32115 32228 2.07

6 59362 5.00 59396 59462 3.23

As the results show, hybrid algorithm obtains very good solutions in a very short time comparing to exact method. However, as the dimension of the problem grows the solution quality of the hybrid algorithm decreases slightly. In total, considering the dimensions of the real world problems, it seems reasonable to use the hybrid algorithm for a high quality solution, which can be obtained in short time.

7.3 Design and Outputs of Inventory Management Module

Similar to other modules of the decision support system, the inventory management module is also defined by a set of inputs and outputs. Figure 28 shows the inputs and outputs of the inventory management module. The outputs are the material schedule and supply schedule. The material schedule turns the schedule into a timetable that specifies at what times different stations should be fed by what types of materials. 130

The supply schedule determines the amount of materials that should be ordered for each supplier in each time period.

Figure 28. Input and outputs of inventory management module 131

8 EXPERIMENTATION

In this chapter, the process of implementing the proposed decision support system in a real setting will be explained. For this purpose, a textile and apparel factory has been chosen. The reason for choosing the textile industry is the volatile and highly fluctuating demand patterns in this area of commerce. In addition to the seasonal pattern of demand in the textile industry, the complexity of the production line--in terms of number of machines, operators, and activities performed--is another reason that it is being chosen as the test ground. The goal is to show how the proposed decision support system can help in choosing the best strategy when there are several decisions to be made in an uncertain environment.

8.1 Introducing the Textile Factory and Shop Floor

The textile factory chosen as the test ground is in the women’s clothes market and has five production classes, including jackets, raincoats, winter coats, trousers, and shirts.

For each production class, a separate line is set up. Each class has several designs for each year and new designs are introduced to the shop floor each season. Some of the classes, such as winter coats and raincoats, are produced in a limited time during the year and have a highly seasonal demand. The production capacity of these classes is shared with other products during the low-demand seasons.

In this research, the winter coat line is chosen as a pilot for implementing the decision support system. The planning period is supposed to start from November 1st,

2014, and consists of four periods. Each period is considered to be one month, and hence, the planning horizon will be ending on March 1st, 2015. The reason for choosing this time 132 interval is because the company introduces its new winter coats into the market around the end of November and the demand starts to decline sharply at the end of February. As the demand decreases, the company has to reduce the prices in order to sell more winter coats. The coats that remain unsold are not kept for the next year and are sold at a salvage price. Fashion trends are among the main reasons that prevent a textile company from stocking its products for the next year.

Although the winter coats have different designs, all of them follow the same pattern in terms of production and have the same main parts. A winter coat consists of a

“front”, “back”, “sleeve”, “hem”, “lining” and “collar”. Each part of the coat is produced in a separate station. Hence, the production line has six stations that manufacture the different parts of coats. In addition to these six stations, there are five more stations called

“support”, “supplementary lining”, “body assembly”, “supplementary 1” and

“supplementary 2”. At the support station, the initial and small parts of a coat--such as pockets and belts--are produced and sent to the stations where they are needed. In body assembly, the main parts of the coats are attached together. In supplementary lining, the coats’ lining is attached to the main body, while in supplementary 1 and 2, the final touches on producing a coat are done. These preparations mainly include ironing, covering, and packaging.

To explain the products and production line in more detail, the process of manufacturing one winter coat as well as the production line configuration will be described. The product chosen for this purpose is known by the code 832 in the firm. The first set of activities for manufacturing coat 832 is performed in the support station. For 133 this purpose, different fabric parts, zippers, buttons, and pockets that are cut in the proper sizes enter the support station. Figure 29 shows the material needed and the activities involved in the support station for producing coat 832. Dark circles depict the input and output of the support station in terms of material, while the round-cornered rectangular shapes show the activities and their time in seconds.

15 10 5 5 cutting ironing flapping sewing Ready to Right button use piece piece

2 tagging Right upper 27 20 15 hem aligning dressing sticking

Right hem

Right upper hem layer Figure 29. The material needed and activities involved in “support” station for producing coat 832

To perform the activities in the support station, a specific number of operators and machines are needed. Figure 30 shows the standard configuration of the support station, which is consists of three operators, four sewing machines, one iron table and four tables for storing the works-in-progress (WIP).

134

20000.00 5000.00 5000.00 15000.00 15000.00 10000.00

Ironing table

Sewing machine Sewing machine 10000.00 Sewing machine Sewing Swing machine Swing 15000.00 15000.00

10000.00 10000.00

Figure 30. Support station standard configuration

In this configuration, two of the operators work with two sewing machines each and the ironing table is controlled by one operator. The size of station’s equipment and the space required is shown in the figure.

The output of the support station, in combination with the other material inputs depicted in Figure 31, compose the inputs to the front station. The front of coat 832 has two parts, namely the right and left front. These two parts are produced in the front station.

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80 sewing Ready to use piece

Right hem

2 Right front 60 70 tagging middle ironing sewing 20 15 Ready to use dressing sticking right front Right front middle layer

65 20 70 70 Left pouch Left ticket Seam sewing sewing sewing sewing 2 tagging 20 15 Right front corner dressing sticking Right pocket Right pocket pouch ticket

Right front corner layer

Right zipper 2 tagging Left upper hem 20 15 dressing sticking Left upper hem layer

80 60 50 2 sewing ironing sewing tagging Ready to 20 15 Left front use left front middle dressing sticking

65 20 70 70 Left front Left button Pocket pouch Pocket ticket piece Seam sewing Zipper sewing middle layer sewing sewing

2 tagging Left pocket Left pocket 20 15 Left front pouch ticket corner dressing sticking

Left front corner layer

Left zipper Figure 31. The materials needed and activities involved in “front” station for producing coat 832

Note that in this specific coat model, the support station is the predecessor of the front station. However, the support station is a predecessor to all of the other stations.

Figure 32 shows the standard configuration of the front station. The configuration of the front station is very similar to a support station. However, the sewing machine types are different.

136

20000.00 5000.00 5000.00 15000.00 15000.00 10000.00

Ironing Table Sewing machine Sewing machine 10000.00 Sewing machine Sewing machine 15000.00 15000.00

10000.00 10000.00

Figure 32. Front station standard configuration

Figure 33 depicts the materials needed and activities involved in a back station for producing coat 832. In a back station, the back part of coats are sewed together and become ready to be delivered to the next station. Similar to other stations, a back station has a standard configuration. Figure 34 shows the back station standard configuration.

2 tagging Lower back piece 20 15 dressing sticking Lower back piece layer

20 30 10 40 2 Attaching fastener ironing flipping sewing tagging 12 20 15 Upper back piece aligning dressing sticking

70 Upper back sewing piece layer

25 60 54 54 50 50 140 170 45 Attaching ring Seam ironing layer sewing sewing sewing cutting ironing flipping sewing Ready to Back piece use back button piece

2 tagging Ring layer Right back 32 middle sewing 2 tagging Left back middle

2 tagging Right back corner

2 tagging Left back corner Figure 33. The materials needed and activities involved in “back” station for producing coat 832 137

5000.00 15000.00

Sewing machine 10000.00 Ironing table 20000.00 15000.00

10000.00 10000.00 Sewing machine

Figure 34. Back station standard configuration

Figure 35 shows the materials needed and activities involved at a sleeve station for producing coat 832. The diagram has two separate parts for the right and left sleeves.

138

2 tagging 20 Right sleeve bigger piece sewing 2 20 25 30 25 25 tagging Seam ironing Seam ironing Right sleeve sewing sticking sewing smaller piece Ready to use right sleeve

15 2 alligning tagging Right wrist 70 Right sleeve layer wrist sewing

10 10 5 15 Right wrist cutting ironing flipping sewing piece Right wrist button piece

2 tagging Left sleeve 20 bigger piece sewing 2 20 25 30 25 25 tagging Seam ironing Seam ironing Left sleeve sewing sticking sewing smaller piece Ready to use left sleeve

15 2 alligning tagging Left wrist Left sleeve layer 70 wrist sewing 10 10 5 15 Left wrist cutting ironing flipping sewing piece Left wrist button piece Figure 35. The materials needed and activities involved in “sleeve” station for producing coat 832

The configuration of a sleeve station is similar to that of a back station. Figure 36 shows the sleeve station’s standard configuration.

5000.00 15000.00

Sewing machine 10000.00 Ironing table Sewing machine 20000.00 15000.00 10000.00 10000.00

Figure 36. Standard configuration of sleeve station 139

Figure 37 depicts the materials needed and activities involved at a hem station for producing coat 832.

2 tagging

Left hem 25 15 dressing sticking Left hem 20 60 layer sewing sewing hem 2 tags tagging

20 15 Collar back dressing sticking

Collar back layer

2 tagging

45 25 15 Right hem alligning dressing sticking

90 30 17 30 170 70 90 Hem Right hem fastening piercing marking ironing closing openning sewing layer

20 sticking Hem lining Figure 37. The materials needed and activities involved in “hem” station for producing coat 832

Figure 38 shows the standard configuration of a hem station.

20000.00 5000.00 5000.00 15000.00 15000.00 10000.00

Ironing table Sewing machine Sewing machine 10000.00 Sewing machine Sewing machine 15000.00 15000.00

10000.00 10000.00

Figure 38. Standard configuration of hem station 140

Figure 39 depicts the materials needed and the activities involved at a lining station for producing coat 832.

2 tagging Lining right 40 40 25 back middle sewing sewing sewing

2 tagging Lining left back middle

2 tagging Lining left back corner

2 tagging Lining right back corner

2 tagging Lining right 30 30 65 65 10 10 30 front middle sewing sewing sewing sewing Seam sewing Seam sewing sewing

Lining 2 tagging Lining right front corner

2 tagging Lining left 30 front middle sewing 2 tagging 10 Lining left sewing front corner

2 cutting Washing code tage

2 tagging 20 15 Lining right bigger sleeve Seam sewing Seam sewing

2 tagging Lining right smaller sleeve

2 tagging 20 15 Lining left bigger sleeve Seam sewing Seam sewing

2 tagging Lining left smaller sleeve Figure 39. The materials needed and activities involved in “lining” station for producing coat 832

Figure 40 shows the standard configuration of a lining station. 141

5000.00 Sewing machine Sewing machine 15000.00

10000.00 10000.00

10000.00 10000.00 Figure 40. Standard configuration of lining station

Figure 41 depicts the materials needed and activities involved at a collar station for producing coat 832.

142

2 tagging

Upper collar 20 20 15 dressing aligning sticking

Upper collar 10 35 layer ironing sewing

2 tagging 20 30 15 Upper collar edge dressing aligning sticking

60 15 35 70 Upper collar edge layer ironing flipping dressing sewing

collar

2 tagging 20 20 15 Lower collar dressing aligning sticking

Lower 10 35 collar layer ironing sewing

2 tagging 20 30 15 Lower collar edge dressing aligning sticking

Lower collar edge layer Figure 41. The materials needed and activities involved in “collar” station for producing coat 832

Figure 42 depicts the standard configuration of a collar station.

5000.00 15000.00

Sewing machine 10000.00 Ironing table Sewing machine 20000.00 15000.00 10000.00 10000.00

Figure 42. Standard configuration of collar station

143

Figure 43 shows the materials needed and activities involved at a body assembly station for producing coat 832. At a body assembly station the main parts of the coat are sewed together.

Ready to use right front 70 80 65 65 40 40 70 10 10 50 50 sewing sewing sewing sewing sewing sticking ironing sewing sewing Seam sewing Seam sewing Ready to use Body left front

Ready to use foam foam Left sleeve Right sleeve layer back Figure 43. The materials needed and activities involved in “body assembly” station for producing coat 832

Figure 44 depicts the standard configuration of a body assembly station.

20000.00 5000.00 5000.00 15000.00 15000.00 10000.00

Ironing table Sewing machine Sewing machine 10000.00 Sewing machine Sewing machine 15000.00 15000.00

10000.00 10000.00

Figure 44. Standard configuration of body assembly station

Figure 45 shows the materials needed and activities involved at a supplementary lining station for producing coat 832.

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Hem 140 60 185 ironing aewing sewing Complete Lining

Lining Figure 45. The materials needed and activities involved in “supplementary lining” station for producing coat 832

Figure 46 depicts the standard configuration of a supplementary lining station.

5000.00 15000.00

Sewing machine 10000.00 Ironing table Sewing machine 20000.00 15000.00 10000.00 10000.00

Figure 46. Standard configuration of supplementary lining station

Figure 47 shows the materials needed and activities involved at “supplementary

1” station for producing coat 832.

145

Body

150 35 250 130 30 65 45 45 30 60 130 90 260 120 180 170 45 Button sewing sewing ironing flipping sewing sewing sewing sewing tucking sewing sewing ironing sewing Seam sewing dressing sewing aligning Semi finished good

Complete Collar lining Figure 47. The materials needed and activities involved in “supplementary 1” station for producing coat 832

Figure 48 shows the standard configuration of a supplementary 1 station. Note that at a supplementary 1 station that is performing ironing activities, two operators are needed.

10000.00 20000.00

15000.00

Ironing table

Sewing machine 15000.00 Sewing machine 15000.00 Sewing machine

Sewing machine Sewing machine 10000.00

Sewing machine 10000.00 10000.00 15000.00

15000.00 Figure 48. Standard configuration of a supplementary 1 station

Figure 49 shows the materials needed and activities involved at a “supplementary

2” station for producing coat 832. Note that one of the activities depicted in Figure 49 is shown in a diamond form, which is a control activity. Although the quality of the products is monitored throughout the entire production line, since this specific control activity is performed by the operators of the shop floor, it is included in the diagram. 146

55 360 15 30 480 60 200 15 25 Control Covering Blowing Tag hanging buttoning ironing ironing 240 sewing piercing alining Semi finished Coat 832 good Figure 49. The materials needed and activities involved in “supplementary 2” station for producing coat 832

Figure 50 depicts the standard configuration of a supplementary 2 station.

15000.00 10000.00 20000.00

Mannequin iron

Ironing table Sewing machine 15000.00

20000.00

Covering table Covering table

Figure 50. Standard configuration of supplementary 2 station

The shop floor stations are designed flexibly and can adapt to new product requirements. In addition, it is possible to adjust the production capacity by adding or reducing the number of operators at each station. However, due to human resource constraints, only 32 operators can be assigned to the production line. Figure 51 shows the overall shop floor layout and arrangement of stations.

147

Front 15000.00 Collar 15000.00 Sleeve 15000.00 Body assembly Lining Supplementary 1 Supplementary 2

11000.00 11000.00 5000.00 11000.00 5000.00 11000.00 5000.00 11000.00 11000.00 11000.00 11000.00

20000.08 5503.20 5503.20 5503.20 5503.20 5000.00 10000.00 10000.00

5000.00

11000.00 20000.00

5503.20 5503.20

5503.20 5000.00 11000.00 11000.00 5000.00 10000.00 11000.00 5000.00 11000.00 5000.00 11000.00

Back Support Hem Supplementary lining 15000.00 15000.00 Figure 51. Overall shop floor layout

8.2 Introducing the Products

For the planning periods, the factory has decided to introduce 30 designs for coats. Each design for a coat includes several colors and sizes. Note that although a coat may be produced with different colors and sizes, in practice--for planning and scheduling purposes--each coat is considered as one product regardless of its colors and sizes. Each product has a unique code in the production line, and in this research, the products will be recognized by their codes as well. The codes start from 831 and go up to 860 (the steps involved in the production of coat 832 are explained in detail in section 8.1‎ ).

These 30 coats’ designs are chosen based on the fashion market situation and are expected to have the highest favorability among customers. However, their demand is estimated to be different for each product based upon the price. In this regard, the sales department estimates a minimum and maximum demand for each product in each period, based upon the price points. Table 14 lists the price points chosen by the sales department for each product in each period.

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Table 14: Price points for each product in each period, suggested by sales department Period 1 Period 2 Period 3 Period 4 Product Pr. Pr. Pr. Pr. Pr. Pr. Pr. Pr. Pr. Pr. Pr. Pr. Code 1 2 3 1 2 3 1 2 3 1 2 3 831 93 104 108 93 104 108 75 84 88 53 59 62 832 97 99 110 97 99 110 75 82 88 50 59 63 833 97 105 111 97 105 111 77 81 86 50 57 62 834 95 103 106 95 103 106 74 80 87 52 58 60 835 95 100 108 95 100 108 74 82 88 51 55 61 836 96 99 108 96 99 108 76 84 86 54 55 62 837 95 101 107 95 101 107 76 83 87 54 58 61 838 93 101 108 93 101 108 76 83 87 52 58 60 839 97 105 111 97 105 111 75 81 85 52 55 60 840 95 103 106 95 103 106 75 80 86 53 59 64 841 96 100 106 96 100 106 75 84 85 54 59 63 842 95 99 110 95 99 110 78 81 86 51 57 61 843 96 99 107 96 99 107 77 82 85 50 57 62 844 94 105 108 94 105 108 74 84 85 52 59 60 845 95 99 106 95 99 106 77 84 87 50 55 61 846 97 99 108 97 99 108 76 84 87 53 56 63 847 93 103 106 93 103 106 76 80 87 53 58 61 848 95 105 108 95 105 108 77 80 85 52 56 64 849 95 104 107 95 104 107 77 83 88 54 56 63 850 97 100 107 97 100 107 76 83 88 52 56 63 851 97 103 109 97 103 109 78 84 87 50 57 62 852 96 103 109 96 103 109 77 82 88 52 59 60 853 93 100 106 93 100 106 74 83 85 50 59 60 854 93 100 110 93 100 110 76 81 86 51 56 64 855 93 100 107 93 100 107 76 81 88 53 57 63 856 96 99 108 96 99 108 77 82 88 52 58 63 857 93 105 106 93 105 106 77 83 85 54 57 62 858 96 99 109 96 99 109 75 84 85 50 59 61 859 96 103 110 96 103 110 78 83 85 52 59 62 860 94 103 106 94 103 106 75 81 86 52 56 63

For each product’s price point in each period, the sales department estimates a minimum and maximum demand. This estimation is based upon previous years’ 149 experience and consulting with design department experts. Table 15 lists the minimum and maximum demand for each product per price point in period 1.

Table 15: The min. and max. demand for each product per price point in period 1 Price 1 Price 2 Price 3 Min Max Min Max Min Max 204 293 173 250 151 223 207 304 172 247 147 224 213 296 168 249 150 224 212 307 166 246 150 221 207 298 172 250 150 217 198 308 167 247 150 224 208 292 168 251 149 218 200 300 172 249 149 222 197 291 169 251 148 224 206 296 169 247 147 216 208 303 173 247 150 224 202 308 170 246 151 224 210 300 165 248 150 219 212 295 170 248 150 220 208 294 168 250 150 223 203 308 168 250 150 223 195 292 171 250 146 219 201 296 168 250 147 222 215 291 168 251 148 216 214 298 169 246 147 222 206 291 170 251 147 223 197 304 171 247 148 219 200 298 171 246 148 219 211 308 166 247 151 223 215 300 165 251 148 218 195 308 168 248 148 220 211 310 173 248 149 218 195 291 165 246 146 217 201 293 170 247 148 222 201 293 166 246 150 216 150

Table 16 lists the minimum and maximum demand for each product per price point in period 2.

Table 16: The min. and max. demand for each product per price point in period 2 Price 1 Price 2 Price 3 Min Max Min Max Min Max 240 459 205 341 188 290 248 444 191 338 182 291 252 445 185 347 186 292 259 430 201 355 176 284 244 456 200 354 188 286 260 448 207 351 186 288 252 453 186 337 185 293 243 446 206 350 179 281 241 456 199 348 174 303 249 435 203 352 173 298 256 448 206 351 178 283 241 441 191 356 184 294 243 436 199 350 180 289 251 452 187 349 177 292 248 444 208 352 184 284 258 443 196 344 183 288 243 458 199 357 186 304 256 447 195 354 183 293 249 448 205 342 177 283 246 447 186 338 188 295 252 450 207 350 188 284 253 460 195 349 187 291 256 446 182 347 176 282 242 449 183 337 180 295 247 444 192 356 174 288 242 446 181 337 185 291 254 432 195 349 182 297 240 460 205 342 176 305 253 451 181 335 187 305 260 433 208 338 182 288 151

Table 17 lists the minimum and maximum demand for each product per price point in period 3.

Table 17: The min. and max. demand for each product per price point in period 3 Price 1 Price 2 Price 3 Min Max Min Max Min Max 249 347 185 246 168 232 251 351 177 248 175 224 251 355 183 249 167 235 248 348 177 249 177 222 249 347 181 252 169 235 251 345 185 252 177 224 248 355 177 247 172 226 252 352 180 251 177 227 247 352 186 249 168 237 252 345 180 247 171 224 250 347 185 248 168 224 253 345 182 251 174 221 253 356 184 252 167 224 252 348 178 252 176 230 252 352 184 247 167 236 252 356 186 252 168 225 252 346 178 247 171 237 250 343 184 248 168 224 248 345 186 246 166 227 252 342 186 249 166 237 253 343 181 250 176 230 247 347 182 252 166 231 248 348 185 251 177 221 248 355 185 252 175 234 249 348 182 251 167 224 247 343 179 247 166 237 249 354 182 250 168 232 252 349 178 248 171 225 253 344 186 247 168 224 253 352 179 252 173 224 152

Table 18 lists the minimum and maximum demand for each product per price point in period 4.

Table 18: The min. and max. demand for each product per price point in period 4 Price 1 Price 2 Price 3 Min Max Min Max Min Max 101 176 80 137 46 77 99 169 83 126 52 71 100 174 82 130 46 71 103 169 79 132 54 81 104 172 83 127 53 76 97 173 75 124 49 75 100 175 81 133 50 71 97 175 85 134 51 74 100 175 78 125 45 76 101 174 75 126 45 74 96 170 76 128 44 78 102 169 85 126 45 71 103 173 81 124 48 82 95 172 78 131 54 79 99 175 81 125 49 72 103 167 84 127 46 72 104 166 85 129 49 75 96 168 84 136 47 74 104 171 78 137 45 81 97 176 78 133 45 78 98 170 79 136 52 77 96 176 77 134 47 71 102 169 82 127 48 76 103 167 75 137 45 71 96 168 80 137 46 81 101 167 81 132 51 71 104 167 81 133 50 77 100 168 75 132 48 79 100 166 83 135 45 71 104 170 75 134 45 80 153

8.3 Estimating the Costs and Resource Constraints

Using the method described for cost estimation in section 4‎ , production, inventory, and lost sale costs are then estimated. Table 19 lists the estimated costs.

Note that, due to the geometrical similarity of the coats, their inventory cost is estimated to be the same ($2 per item per period). Considering the same logic, each coat occupies one single space in the warehouse and hence, the space consumption coefficient for all of the coats is 1.

The coat's factory warehouse has enough capacity for stocking 5000 coats.

Considering that each station in the production line is designed to deliver output in a maximum of 5 minutes and there are 10 working hours per day, the production capacity is 120 items per day. Hence, with 25 working days in a month, the monthly production capacity is products. The management can assign budget for production of a total 15000 coats, considering the average production costs. Hence, the budget constraint is not expected to be active in the planning model.

154

Table 19: Estimated production, inventory, and lost sale costs for products Lost Product Production Inventory Sale Code Cost Cost Cost 831 43 2 11 832 43 2 11 833 49 2 9 834 49 2 9 835 48 2 9 836 41 2 11 837 47 2 10 838 41 2 11 839 46 2 10 840 50 2 9 841 50 2 9 842 43 2 11 843 40 2 11 844 44 2 10 845 41 2 11 846 41 2 11 847 48 2 9 848 40 2 11 849 46 2 10 850 41 2 11 851 44 2 10 852 44 2 10 853 44 2 10 854 43 2 11 855 49 2 9 856 45 2 10 857 40 2 11 858 42 2 11 859 49 2 9 860 41 2 11

155

8.4 Pricing, Planning and Price of Robustness

Based on the data introduced in sections ‎8.2 and 8.3‎ , the first step in implementing the decision support system is to calculate the prices and then plan for the horizon. Using the mathematical model and technique introduced in section ‎5, the problem is solved using CPLEX software that yields the exact solution and the proposed unconscious search where the uncertainty budget parameter is zero, i.e. . Note that when , all the demands are considered to be exact, and hence no uncertainty is considered in the problem.

CPLEX takes more than 11 minutes and terminates the solving procedure due to an out-of-memory error. However, unconscious search (US) finds a good solution in less than 10 seconds. Note that the memory of the computer used for this research is 12.0 GB, and the processor has a core i7 3.40 GHz.

The value of the objective function obtained by US, which is the maximized profit by a pricing and planning agent, is equal to $482,978. Table 20 lists the prices obtained by the pricing and planning module for each period. For the first three periods, all the prices are chosen to be at the highest possible. However, as the demand decreases in the last period, most of the prices chosen are less than the highest possible. This trend tends to go well with intuition.

Table 21 list the production plan for each product in each period. Some products are planned to be produced in specific periods. However, this trend does not apply to the last period, where all the products are placed in the production plan. The reason may be 156 that, as the demand falls, the profit margin of all the products gets closer to each other, and hence, it is profitable to produce all products.

Table 20: Prices obtained by pricing and planning module for each period ($) Period Period Period Period Product 1 2 3 4 831 108 108 88 59 832 110 110 88 59 833 111 111 86 62 834 106 106 87 58 835 108 108 88 61 836 108 108 86 54 837 107 107 87 58 838 108 108 87 58 839 111 111 85 60 840 106 106 86 64 841 106 106 85 59 842 110 110 86 57 843 107 107 85 57 844 108 108 85 59 845 106 106 87 55 846 108 108 87 56 847 106 106 87 58 848 108 108 85 56 849 107 107 88 63 850 107 107 88 56 851 109 109 87 57 852 109 109 88 59 853 106 106 85 59 854 110 110 86 56 855 107 107 88 63 856 108 108 88 58 857 106 106 85 54 858 109 109 85 59 859 110 110 85 59 860 106 106 86 56 157

Table 21: Production plan obtained by pricing and planning module Period Period Period Period Product 1 2 3 4 831 187 153 200 109 832 186 237 200 105 833 0 0 0 59 834 0 0 0 106 835 0 0 0 65 836 187 237 201 135 837 0 0 0 107 838 186 230 202 110 839 32 0 0 61 840 0 0 0 60 841 0 0 0 102 842 188 239 198 106 843 185 235 196 103 844 0 0 0 105 845 187 234 202 103 846 187 236 197 106 847 0 0 0 107 848 185 238 196 110 849 0 0 0 63 850 185 242 202 106 851 185 0 5 108 852 184 0 199 106 853 0 0 0 105 854 187 238 205 106 855 0 0 0 64 856 0 0 0 107 857 184 240 200 136 858 182 241 198 104 859 0 0 0 109 860 183 0 199 105

158

Due to inventory costs, the plan obtained by the pricing and planning module is arranged in a way to keep zero inventory at the end of the month. Thus, the sales plan is expected to be similar to the production plan.

One interesting aspect of the pricing and planning module’s output is the ability to calculate the increased profit due to the increased capacity. In other words, it is possible to ask how much the profit could be increased by increasing the production capacity.

Answering this question can help management to understand and calculate the most profitable amount of investment in production utilities and machines.

To obtain the relationship between capacity and profit, the pricing and planning module has calculated the profit taking into account the different production capacities.

Figure 52 depicts the relationship between production capacity and profit. As is expected, by increasing the production capacity, the profit increases. However, the amount by which the profit is increased has a decaying slope until it reaches the zero point, when production capacity is approximately 11000.

1400000 1200000 1000000 800000

Profit 600000 400000 200000 0 0 2000 4000 6000 8000 10000 12000 14000 Production Capacity (per period)

Figure 52. Increase in profit as the production capacity increases 159

To consider the demands associated with prices in an uncertain setting, the uncertainty budget parameter needs to be greater than zero, i.e. . In this case, although the uncertain demand has been taken into consideration, the optimum solution will be decreased. The difference between the exact problem optimum value and the uncertain problem optimum solution is the price of robustness. From a managerial point of view, the price of robustness is the cost that the system accepts in order to handle the uncertainty robustly.

To evaluate the price of robustness, the best value of the objective function is calculated per the different values of . Figure 53 shows the price of robustness as the uncertainty budget parameter increases. As expected, the graph increases monotonically as the uncertainty budget parameter increases. According to Figure 53, if a worst-case scenario is considered for this problem, $4339 will be imposed on the best-found value of the objective function, which is less than 1% of the deterministic objective function value. As the increases, the probability of a constraint to be violated due to uncertainty decreases. This probability becomes zero when .

160

5000 4500 4000

3500 3000 2500 2000

Price of Robustness Price 1500 1000 500 0 0 20 40 60 80 100 120 140 Uncertainty Budget Parameter

Figure 53. Price of robustness per different values of uncertainty budget parameter

To proceed to the scheduling module of the proposed decision support system, it is necessary to choose a plan with a specific level of robustness. The management of the textile firm believes that considering the worst-case scenario does not impose too much expense, and since it has considered the uncertainty fully, the worst-case scenario is chosen for the production plan. Table 22 tabulates the production plan for the worst-case scenario for each period.

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Table 22: Production plan for worst-case scenario Period Period Period Period Product 1 2 3 4 831 187 0 200 109 832 186 237 200 105 833 0 0 0 59 834 0 0 0 106 835 0 0 0 65 836 187 237 201 135 837 0 0 0 107 838 186 230 202 110 839 186 0 0 61 840 0 0 0 60 841 0 0 0 102 842 188 239 198 106 843 185 235 196 103 844 0 0 0 105 845 187 234 202 103 846 187 236 197 106 847 0 0 0 107 848 185 238 196 110 849 0 0 0 63 850 185 242 202 106 851 185 0 5 108 852 30 0 199 106 853 0 0 0 105 854 187 238 205 106 855 0 0 0 64 856 0 0 0 107 857 184 240 200 136 858 182 241 198 104 859 0 0 0 109 860 183 153 199 105

Table 23 tabulates the chosen prices for each product in each period for the worst- case scenario. 162

Table 23: Chosen prices for each product in each period for the worst-case scenario Period Period Period Period Product 1 2 3 4 831 108 108 88 59 832 110 110 88 59 833 111 111 86 62 834 106 106 87 58 835 108 108 88 61 836 108 108 86 54 837 107 107 87 58 838 108 108 87 58 839 111 111 85 60 840 106 106 86 64 841 106 106 85 59 842 110 110 86 57 843 107 107 85 57 844 108 108 85 59 845 106 106 87 55 846 108 108 87 56 847 106 106 87 58 848 108 108 85 56 849 107 107 88 63 850 107 107 88 56 851 109 109 87 57 852 109 109 88 59 853 106 106 85 59 854 110 110 86 56 855 107 107 88 63 856 108 108 88 58 857 106 106 85 54 858 109 109 85 59 859 110 110 85 59 860 106 106 86 56

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8.5 Scheduling

Using the output of the pricing and planning module and other necessary inputs described in section 6‎ , the scheduling module can optimize the job sequence. The products and their production plan obtained in the pricing and planning module are considered jobs. The beginning and finish time of each time period is considered the release time and due date of the jobs. Hence, if 187 units of coat 831 are to be produced in the first period, the beginning and finish time of the first period are considered as the release time and due date of producing these 187 units.

The working hours of the shop floor are from 9:00 to 19:00, and the maintenance times are scheduled during non-working hours. Thus, the only valid interval for scheduling the tasks is from 9:00 to 19:00. Note that having a working timeline with some time intervals that are not allowed to be scheduled, as well as jobs with various release times, can dramatically add to the complexity of the scheduling problem.

For each product, it is necessary to define the operation chart and have its cycle times on each shop floor station. In the proposed decision support system, this is possible by a graphical user interface that gives the user the ability of defining operations charts by drawing the process flow. Figure 54 shows the user interface for defining the operations chart for coat 832. As can be observed in Figure 54, it is possible to define the operations chart of the product in a network format. In each station, the list of necessary activities with their cycle times, required human resources, materials, and machines are stored. Hence, it is possible to calculate processing times and the necessary resources for job scheduling. All of the cycle times are between 200 to 300 seconds for each product 164 and station. In addition, due to labor-intensive nature of the production processes, each processing time has to be given some leeway, with 20 seconds as the maximum possible deviation from the average. Thus, the processing time for each product in each station has a triangular distribution.

Setup times for each product can be defined dependently. However, in this case the setup times are independent and very small. Thus, it is possible to ignore them. Note that, the method used in the scheduling module can handle dependent setup times as well.

Figure 54. User interface for defining operation process of coat 832

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In addition to the inputs for optimizing the schedule, it is necessary to define the objective function of the scheduling module as well. Three objective functions are considered in this case; make span, total finish time, and total tardiness. Figure 55 shows the user interface of the decision support system in which the jobs, their due dates, release times, weights, and objective function can be defined.

Figure 55. User interface for defining the jobs and choosing the objective function

For the case chosen, the objective function preferred by the management is make span. Note that tardiness is not chosen due to the low lost sale costs for each product.

However, in a different industry such as automotive, it seems logical to use total tardiness as an objective function due to the high lost sale costs associated with products and the high costs of stopping the manufacturer production line by the supplier due to late production.

Considering the make span as the objective function, the scheduling module optimizes the sequence of the jobs in order to minimize the make span. In total, 77 products with all their respective production stations, activities, and necessary resources, 166 need to be scheduled in a four-month period. After running the scheduling algorithm, it takes approximately 20 seconds to come up with a schedule. Note that the user can accept, reject, or modify the schedule. Figure 56 shows the schedule for three days – i.e.

November 8th, 9th, and 10th. Each color shows a product.

After scheduling the products, no delay was observed in the jobs, and the total tardiness was zero. In each time period, approximately 20% of the time is not scheduled, which is due to the possible variations in processing times and unscheduled stoppages.

This is completely in accordance with the historical performance of the factory. This shows that the scheduling module has successfully considered the probabilistic nature of the tasks.

th th th Figure 56. User interface for scheduling November 8 , 9 ., and 10

8.6 Inventory Management

In each winter coat, three types of fabric are used for the outer layer, the lining, and the middle layer. Since the outer layer and the lining are visible, their color needs to be matched. However, the middle layer is invisible and can be any color. In total, 21 167 different fabrics are chosen for the designed winter coats, among which 10 are for the outer layer, 10 are for the lining, and one is for the middle layer. Table 24 lists the fabric consumption for each product. (The unit of consumption chosen is the yard.) Note that, although there are other materials such as buttons and threads necessary for producing a coat, since their prices are very low compared to the fabrics, they are not included in the inventory management module.

There are five suppliers that provide the fabrics to the factory. However, since these suppliers are located in different regions, the ordering costs are different. Note that for each order, it is necessary that a team from the design department go to the supplier site and introduce the necessary quality specifications. Hence, the main cost associated with ordering a fabric is the cost of relocating the design team. The ordering cost of the first and second suppliers is approximately $500, while for the rest of the suppliers, this cost is approximately $300.

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Table 24: Fabric consumption for each product (yard) Outer Middle Product Lining Layer Layer 830 3.1 2.4 1.8 831 2.9 2.2 1.6 832 2.8 2.1 1.5 833 3.2 2.5 1.9 834 2.5 1.8 1.2 835 2.8 2.1 1.5 836 2.9 2.2 1.6 837 2.6 1.9 1.3 838 2.6 1.9 1.3 839 2.9 2.2 1.6 840 2.9 2.2 1.6 841 2.8 2.1 1.5 842 2.9 2.2 1.6 843 2.8 2.1 1.5 844 3 2.3 1.7 845 2.9 2.2 1.6 846 3.1 2.4 1.8 847 2.5 1.8 1.2 848 2.6 1.9 1.3 849 2.9 2.2 1.6 850 2.7 2 1.4 851 2.7 2 1.4 852 3.1 2.4 1.8 853 3.1 2.4 1.8 854 3.1 2.4 1.8 855 2.9 2.2 1.6 856 2.5 1.8 1.2 857 2.6 1.9 1.3 858 3.1 2.4 1.8 859 2.5 1.8 1.2

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The inventory cost of all the fabrics is approximately $0.4. All of the suppliers offer nearly the same purchasing price. However, there are small variations. Table 25 lists the purchasing cost of a unit of each fabric from each supplier.

Table 25: Purchasing cost of each fabric from different suppliers Supplier Supplier Supplier Supplier Supplier Fabric 1 2 3 4 5 1 2 2 2.1 2 2 2 1.8 2.1 2.1 1.8 2 3 1.9 2.1 2 1.9 1.9 4 1.8 2.1 2.1 1.8 2 5 1.8 2.1 2.2 1.8 2 6 2 2.1 2.1 2 2.1 7 1.9 2.1 2 1.8 2 8 2 2.1 2 1.8 2 9 1.8 2 2 2 2.1 10 1.9 2.1 2.1 2 2 11 1.9 1.9 2.2 1.9 2 12 1.8 1.9 2 1.9 2 13 1.9 1.9 2.1 1.8 2 14 1.9 2.1 2 1.9 2 15 1.8 1.9 2.1 1.9 1.9 16 1.9 2 2.1 1.9 2 17 1.9 2 2.2 1.9 1.9 18 1.9 1.9 2.2 2 2 19 1.8 2.1 2.1 1.8 2 20 2 2 2.2 2 2 21 2 1.9 2.1 1.9 2.1

In addition to the costs, it is necessary to determine the demand for each fabric.

Using the fabric consumption listed in Table 24 and the production plan in each period, it is possible to take the output of the production plan and schedule it into the material plan. 170

Table 26 lists the estimated consumption of each fabric in each period. The raw material warehouse of the factory has enough capacity for storing 15000 yd of fabrics. The minimum ordering amount for each fabric is considered to be 500 yd.

Table 26: Consumption of each fabric in each period Period Period Period Period Fabric 1 2 3 4 1 832.6 832.97 836.25 844.72 2 832.6 832.97 836.25 844.72 3 832.6 832.97 836.25 844.72 4 832.6 832.97 836.25 844.72 5 832.6 832.97 836.25 844.72 6 832.6 832.97 836.25 844.72 7 832.6 832.97 836.25 844.72 8 832.6 832.97 836.25 844.72 9 832.6 832.97 836.25 844.72 10 832.6 832.97 836.25 844.72 11 622.6 622.97 626.25 636.26 12 622.6 622.97 626.25 636.26 13 622.6 622.97 626.25 636.26 14 622.6 622.97 626.25 636.26 15 622.6 622.97 626.25 636.26 16 622.6 622.97 626.25 636.26 17 622.6 622.97 626.25 636.26 18 622.6 622.97 626.25 636.26 19 622.6 622.97 626.25 636.26 20 622.6 622.97 626.25 636.26 21 442.6 442.97 446.25 457.58

After feeding the necessary inputs into the inventory management module and running the optimization program, the optimum material plan for each period is obtained 171 with an objective function value of $138101.9. Table 27 shows the material plan for each fabric that needs to be ordered by a specific supplier in periods 1 and 2.

Table 27: Material plan for each fabric that needs to be ordered by a specific supplier in periods 1 and 2 Period 1 Period 2 Fabric S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 1 0 0 0 832.6 0 0 0 0 0 832.97 2 0 0 0 832.6 0 0 0 0 832.97 0 3 0 0 0 0 832.6 0 0 0 0 832.97 4 0 0 0 832.6 0 0 0 0 832.97 0 5 0 0 0 832.6 0 0 0 0 832.97 0 6 0 0 0 832.6 0 0 0 0 832.97 0 7 0 0 0 832.6 0 0 0 0 832.97 0 8 0 0 0 832.6 0 0 0 0 832.97 0 9 1665.6 0 0 0 0 0 0 0 0 0 10 0 0 0 832.6 0 0 0 0 832.97 0 11 0 0 0 1245.6 0 0 0 0 0 0 12 0 0 0 1245.6 0 0 0 0 0 0 13 0 0 0 1245.6 0 0 0 0 0 0 14 0 0 0 1245.6 0 0 0 0 0 0 15 0 0 0 1245.6 0 0 0 0 0 0 16 0 0 0 1245.6 0 0 0 0 0 0 17 0 0 0 0 1245.6 0 0 0 0 0 18 0 0 0 1245.6 0 0 0 0 0 0 19 0 0 0 1245.6 0 0 0 0 0 0 20 0 0 0 0 1245.6 0 0 0 0 0 21 0 0 0 885.57 0 0 0 0 0 0

Table 28 shows the material plan for each fabric that needs to be ordered by a specific supplier in periods 3 and 4.

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Table 28: Material plan for each fabric that needs to be ordered by a specific supplier in periods 3 and 4 Period 3 Period 4 Fabric S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 1 0 0 0 0 836.25 0 0 0 0 844.72 2 0 0 0 836.25 0 0 0 0 844.72 0 3 0 0 0 0 836.25 0 0 0 0 844.72 4 0 0 0 836.25 0 0 0 0 844.72 0 5 0 0 0 836.25 0 0 0 0 844.72 0 6 0 0 0 836.25 0 0 0 0 844.72 0 7 0 0 0 836.25 0 0 0 0 844.72 0 8 0 0 0 836.25 0 0 0 0 844.72 0 9 1680.97 0 0 0 0 0 0 0 0 0 10 0 0 0 836.25 0 0 0 0 0 844.72 11 0 0 0 1262.51 0 0 0 0 0 0 12 0 0 0 1262.51 0 0 0 0 0 0 13 0 0 0 1262.51 0 0 0 0 0 0 14 0 0 0 1262.51 0 0 0 0 0 0 15 0 0 0 1262.51 0 0 0 0 0 0 16 0 0 0 1262.51 0 0 0 0 0 0 17 0 0 0 0 1262.51 0 0 0 0 0 18 0 0 0 1262.51 0 0 0 0 0 0 19 0 0 0 1262.51 0 0 0 0 0 0 20 0 0 0 0 1262.51 0 0 0 0 0 21 0 0 0 903.83 0 0 0 0 0 0

One of the most important parameters regarding the objective function value is the warehouse capacity. Figure 57 demonstrates the relationship of the objective function and the warehouse capacity. As the warehouse capacity increases, the value of the objective function decreases monotonically. However, having a warehouse capacity of more than 8000 yd of fabric has no effect on the value of the objective function.

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139400

139200

139000

138800

138600

Objectve Function 138400

138200

138000 0 2000 4000 6000 8000 10000 12000 Warehouse Capacity

Figure 57. Value of the objective function vs. warehouse capacity

8.7 Performance Evaluation of the System

The results shown in this chapter are those obtained before the planning horizon.

However, due to the fluctuating value of the demand and unpredicted production stoppages during the planning periods, it was necessary to revise the plans and schedules as the real situations were realized. Hence, all the modules of the system needed to re- optimize the price, plan, schedule, and material ordering policy in order to maximize the profit. For this purpose, the system needs to be very fast in terms of optimizing and be able to yield good results in the shortest possible time.

To evaluate the efficiency of the system in terms of time, after each run of one of the modules, its respective run time was recorded. The results show that, if the necessary data is stored in the database, it takes less than one minute to run all three modules of pricing and planning, scheduling, and inventory management sequentially. Note that since the cost estimation module does not perform an optimization task, it is not 174 necessary to evaluate its run time. The short run time of the system makes it possible to revise the production plan and schedule as soon as a small change in the system has occurred.

In addition to the time, several other criteria need to be considered to evaluate the efficiency of the system. These criteria have to be comprehensive and include all aspects of performance on a production site. Also, in order to measure the improvement of the production system, it is necessary to compare the situation to a similar period of time when no decision support system was existent.

For this purpose, four different factors--namely, profit per product, overall equipment effectiveness, percentage of the realized schedule, and work-in-process--are chosen and compared to the same period of time from the previous year, when the system was not yet implemented. Note that although the market situation in two years can be completely different, since the production capacity has not changed, these four factors can clearly show how much improvement the system has made using the same amount of resources.

8.7.1 Profit per Product

The main objective of the proposed decision support system is to maximize the profit over a planning horizon. Thus, for assessing its performance, the first criterion is profit. However, measuring the total profit can be misleading. Being in a market with a high demand value when no system is implemented can increase the profit compared to the situation in which the system is installed, but the demand level is very low. Hence, 175 the average profit per product gives a more realistic indicator for evaluating the performance of the system.

According to the sales department of the factory, in the same period – i.e.

November 1st, 2013, to March 1st, 2014– the average profit per each winter coat was

$39.22. This number has increased to $44.07 after implementing the system during the same period one year later. This system has helped to increase the profit per product in several ways. The first impact has occurred where the decision for determining the price was integrated with the production plan, which causes coordination between the market and the capacity. In addition to decision-making integration, considering the demand as a dependent variable of the price and applying a robust method has also helped the sales department to fulfill the demands under different demand-level realizations.

The proposed mathematical model for pricing and planning has enabled the decision makers to evaluate different prices and choose the best one for each period.

Another factor in increasing the profit margin per product is scheduling. Choosing the tardiness as the minimization objective function helped the production line to catch up with the production plan immediately. In the first schedule obtained by the scheduling module, approximately 20% of each period was left with no plan. Although the primary reason of this idle time was to deal with time variations on the shop floor, since the system helped the production line have more control over the activities, nearly half of this time was utilized to increase the capacity for production, and as a result, add to the profit.

Another reason for the added profit was the decreased production costs due to the increased control over the production line. As indicated in section ‎6, the database 176 designed for the scheduling module can store the reports of activities performed on the shop floor and measure the schedule realization percentage. This measurement helps to increase the control over the production line and decrease the unpredicted occurrence of expenses, which itself results in fewer production costs.

8.7.2 Overall Equipment Effectiveness (OEE)

As explained in section ‎6, OEE measures the effectiveness of production machines based on the idle and break down times, combined with the number of defective products and increased cycle times. Although the scheduling module has no direct effect on the OEE, the control section of it--along with maintenance times recorded in the database--helped to improve this indicator. Note that the maximum possible OEE in this case is 41.66%. The reason for this is that only 10 hours a day are working hours, and there is no schedule for the rest of the day. Thus, if all the machines work properly in

a day, the maximum OEE would be . Figure 58 demonstrates the average

OEE of the production line in the planning periods before and after implementing the system.

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25 Before OEE 20 After 15

0 November December January February

Figure 58. OEE of production line before and after implementing the system

Clearly, the OEE has increased in all of the planning periods. However, the trend of the OEE has remained almost the same. In both scenarios, the OEE increased until

January, but declined in February. This shows that, although the control over the schedule has increased, it has not kept the OEE from declining every winter.

8.7.3 Percentage of Realized Schedule

Another evaluation criterion for the proposed decision support system is the percentage of realized schedule. This indicator helps us to understand how realistic the schedule has been and how effectively the schedule is controlled. Figure 59 depicts the percentage of realized schedule before and after implementing the system for each working station.

178

100

90 80 70 60 50 40 Before 30 20 After

Percentage of Realized Schedule 10 0

Figure 59. Percentage of realized schedule before and after implementing the system

The average realized schedule has increased by 10% after implementing the system. Although there is an increase in this indicator, the stations that used to have lower percentages before the implementation have the lowest percentage after implementation as well.

8.7.4 Work-in-Progress (WIP)

For measuring the WIP, the closing time for each working day is considered. For this purpose, at the end of the working hours each day, the amount of the fabric on the production line is counted and considered as WIP. In spite of other performance measures that showed improvement, these measures show that WIP has increased by approximately

10% after implementing the system. This can be the result of an improved OEE or the percentage of a realized schedule. Also, by having more capacity due to increased 179 efficiency, the factory naturally wants to add to the production, and hence, WIP can increase.

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9 CONCLUDING REMARKS AND FUTURE WORKS

To ensure that it retains its maximum profit and market share, a manufacturing company needs to have long-term strategies that are supported by proper short-term objectives. In this regard, it is very important to make integrated decisions in all the strategic, tactical, and operational levels of management. These decisions include--but are not limited to--pricing, production planning/scheduling, and inventory management.

Having an integrated framework for making decisions that can accumulate all these under the umbrella of a unified objective such as profit can greatly contribute to the revenue and market share of manufacturing companies.

In this research, an interactive intelligent decision support system for integrating inventory, planning, scheduling, and revenue management was proposed. The interactivity of the system is due to its ability to convert the demand prediction by an expert into a robust plan and change the plan if the expert provides new information.

Hence, the system needs to interact with the expert to make sure that all the market information is considered. The intelligence of the system is due to its ability to optimize the price, production plan/schedule, and inventory policy in an integrated fashion by using mathematical modeling in order to maximize the profit over a planning horizon.

The proposed decision support system has four distinct modules--namely, financial and cost estimation, pricing and planning, scheduling, and inventory management. Each of these modules work based on the inputs from other modules or experts. In the following sections, the concluding remarks will be stated regarding each module and the implementation of the whole system. 181

9.1 Financial and Cost Estimation Module

The first module of the system is financial and cost estimation. This module takes advantage of an analytical cost estimation method, and its primary goal is to estimate the costs of production, inventory, and lost sales, based upon the expenses realized at each working station of the production line. For this purpose, each station of the shop floor is considered a cost center. Each cost center records its expenses. As an example, if an operator has spent an hour at a station, the labor cost of that hour will be considered for the cost center associated with the station. Based on the time each product spends in each station – i.e. cost center – it is possible to estimate its cost of production. With the same logic considering the warehouse as a station, it is possible to estimate the inventory costs.

The lost sale cost is the potential profit that could be achieved by selling an item but was not realized due to a lack of demand.

The outputs of the financial and cost estimation module are the production, inventory, and lost sales costs. Whenever a new cost is added to one of the cost centers, this part of the system can help to calculate the total resultant costs. Hence, this module plays a very important role in adjusting the parameters of the system so that it continues to make reliable decisions.

9.2 Pricing and Planning Module

In this module, a new mathematical model for determining the price and production plan of products was introduced. In order to take demand fluctuations into consideration, a robust counterpart to the model was formulated that was able to provide the decision makers with a plan immune to demand volume changes. However, this 182 immunity resulted in the loss of a small portion of profit compared to the case where all the demands were considered to be deterministic. For this purpose, the demand is considered to have discrete values with minimum and maximum limits that can be different based on the price.

To solve the mathematical model for large instances which occur in real cases, a two-stage unconscious search and Simplex algorithm was introduced. To evaluate the efficiency of the algorithm, the results were compared against the exact solution for several test problems. While having the same quality, the heuristic solution proved to be more efficient in terms of run time.

The output of the pricing and planning module is a robust plan and a set of optimized prices for each product in each planning period. These outputs were used as an input for the scheduling module.

9.3 Scheduling

Using the outputs of pricing and planning and the inputs defined by users such as setup times, operation charts, machines, timelines, and maintenance times, the scheduling module tries to optimize the sequence of jobs. For this purpose, a two-stage algorithm was introduced. In the first stage of the algorithm, the sequence of jobs were optimized using a variable neighborhood search (VNS) metaheuristic and considered the make span, weighted completion time, and weighted tardiness as the objective functions. In the second stage, each job was scheduled by the order defined in the first stage, using a simulation model in which the processing times were considered to be probabilistic. For 183 determining the schedule of a job, the scarcity of resources such as labor could be considered.

Designing this two-stage algorithm was necessary because the scheduling problem was considered in a general setting where there were dependent setup times, parallel machines at each station with different and probabilistic processing times, and each job could be broken into several parts if necessary. This general framework made it difficult formulate a mathematical model for the problem, and hence, a simulation optimization method was applied. This method was later shown to be very efficient in terms of run time, and was able to yield good-quality solutions in the shortest possible time. The output of the scheduling module was further used as an input for the inventory management module in order to determine the optimum plan for ordering raw material.

9.4 Inventory Management

Using the sequence of jobs optimized in the scheduling module and the BOM defined by the user, the inventory management module finds the best strategy for ordering the raw materials. For this purpose, a new mathematical model was developed.

For solving large instances of the model, a hybrid tabu search and Simplex algorithm was developed. To show the efficiency of the proposed algorithm, several test problems were solved and the results compared against the exact solutions. While having an acceptable solution quality, the results showed considerable efficiency in terms of run time.

9.5 Implementation

To evaluate the performance of all of the modules together, the system was implemented and tested in a textile manufacturing plant which was producing winter 184 coats. After following the results for a period of four months – November 1st to March 1st

– four performance measures of the plant--namely profit per product, overall equipment efficiency (OEE), percentage of realized schedule, and work-in-process (WIP)--were evaluated. The profit per product showed approximately 12% growth. The main reasons for this growth were the higher efficiency in inventory management, production plan and schedule, and the optimum set of prices chosen. In addition, helping to have more control over production line and the resultant reduced production costs was another effective result from improving the profit per product. OEE and percentage of realized schedule were both improved by 5% and 10%, respectively. The main reason for this improvement was the higher control over the production line in the scheduling module.

Although the three previous performance measures were improved, WIP was reported to have increased by approximately 10%. The reason for this increase was the higher equipment efficiency as well as the fact that the scheduling module tried to improve the time efficiency by sacrificing the WIP level. In total, the proposed decision support system was able to meet the promise of optimizing the profit over a planning horizon while being implemented and tested in a real case.

9.6 Limitations and Generalizability

The presented research has several limitations. The first limitation is the experiment environment. Although it is tried to keep the condition of experiment the same as much as possible but some factors such as labor efficiency and demand patterns can potentially affect the results. The attributes of the production system that has been kept constant are time period, production capacity and number of labors. 185

Labor efficiency is the first factor that can potentially affect the results of the implementation. Although it is speculated that the proposed system has helped to control the production line efficiently, but the increase in labor efficiency can also be considered as an independent parameter that increases the efficiency. Demand changes can affect the results as well. Although the demand fluctuations are controlled by introducing a robust optimization model, but a radical shift in demand can affect the implementation results.

Another important issue that needs to be taken into consideration is the applicability limitations of the system and its generalizability. In this research the system is implemented in a textile production line. It is expected that the system can applied to all the textile industries with the same structure. However, it is not possible to apply the presented system to all types of industries.

The presented DSS can generally be applied to industries with discrete production lines. In particular, this system is suitable for jobbing, batch processing and mass production systems. However, the continuous flow systems are not a good fit for the system. In addition to production system configuration, the product price range is also important. The proposed DSS can be applied to the industries with the products that are not considered as luxury. The reason is that these types of products require special constraints to be considered that are not presented in this research. The systems with no- wait constraints in scheduling are not also in the scope of this research.

9.7 Future Works

Several points remain to be explored as future works in this research. The first possible extension of this investigation is to develop a stochastic model in the pricing and 186 planning module where the statistical distribution of the demand is known and comparing it with the robust formulation. This can help to evaluate the superiority of the robust and stochastic approaches under various circumstances.

Applying different approaches to optimize the sequence of the jobs in a scheduling module and testing different metaheuristics and heuristics can also be considered a continuation of the presented research. This can help to find more effective solution methods and reduce the optimality gap while dealing with very large instances.

Using a robust method in the inventory management module where the items of bill of material are subject to deviation can also be a very interesting future work. This will become even more important in industries such as plastics, where the weight of products—and, consequently, the amount of raw material used –can change very often.

Note that in the test case in this research, the variation in the usage of raw material was minimized due to the use of fully automated equipment for cutting the fabrics.

One other possible direction for this research would be to integrate the mathematical models of pricing, planning, and inventory management into one model.

This can result in more efficient production plans, due to a higher degree of integration.

Including the scheduling module in this highly integrated framework is one of the possibilities of future works. For this purpose, it is necessary to provide very fast and efficient solving methods that can be combined with simulation models in order to find high quality solutions. 187

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222

APPENDIX A: CPLEX CODE FOR PRICING AND PLANNING MODULE

//parameters float alpha=...; float K=...; float MM=1000000000;

{string}N=...;

{string}M=...;

{string}JIT=...;

{string}JD=...; int nbPeriod = 4; float gama_d=...;

/////////////////////// float costh[N]; float costp[N]; float costl[N]; tuple table1Struct { string N; float costh;float costp;float costl; };

{table1Struct} table1Data = ...; execute

{

for (var c in table1Data)

{

costh[c.N] = c.costh;

costp[c.N] = c.costp;

costl[c.N] = c.costl; 223

}

/////////////////////// float pu[N][1..nbPeriod]; float gama2[N][1..nbPeriod]; tuple table3Struct { string N;int period;float pu;float gama2; };

{table3Struct} table3Data = ...; execute

{

for (var c in table3Data)

{

pu[c.N][c.period] = c.pu;

gama2[c.N][c.period] = c.gama2;

}

/////////////////////// float lamda[N][M][1..nbPeriod]; float d_hat[N][M][1..nbPeriod]; float d_bar[N][M][1..nbPeriod]; tuple table4Struct { string N;string M; int period; float lamda;float d_hat;float d_bar; };

{table4Struct} table4Data = ...; execute

{

for (var c in table4Data) 224

{

lamda[c.N][c.M][c.period] = c.lamda;

d_hat[c.N][c.M][c.period] = c.d_hat;

d_bar[c.N][c.M][c.period] = c.d_bar;

}

//variable

dvar boolean x[N][M][1..nbPeriod]; dvar boolean y[N][M][1..nbPeriod]; dvar float+ z[N][1..nbPeriod]; dvar float+ w[N][M][1..nbPeriod]; dvar float+ mio_hat[N][M][1..nbPeriod]; dvar float+ s[N][1..nbPeriod]; dvar float+ q[N][0..nbPeriod]; dvar float+ p[N][1..nbPeriod]; dvar float+ p2[N][JD][1..nbPeriod]; dvar float+ noo;

//model maximize 225

sum(i in N,j in M, t in 1..nbPeriod)(w[i][j][t]*lamda[i][j][t]) - sum(i in N, t in 1..nbPeriod)(costh[i]*q[i][t]) - sum(i in N, t in

1..nbPeriod)(costp[i]*p[i][t]) - sum(i in N,j in M, t in

1..nbPeriod)(costl[i]*x[i][j][t]*d_bar[i][j][t]) + sum(i in N,j in M, t in 1..nbPeriod)(costl[i]*w[i][j][t])

- sum(i in N,j in JD, t in 1..nbPeriod)(mio_hat[i][j][t]) - noo*gama_d;

subject to {

//////////////////////////////////////

forall(i in N, j in M, t in 1..nbPeriod)

q[i][t] - q[i][t-1] - p[i][t-1] + s[i][t-1]==0;

forall(i in N)

q[i][0]==0;

forall(i in N, t in 1..nbPeriod)

sum(j in M)x[i][j][t] == 1;

forall(i in N, t in 1..nbPeriod)

p[i][t]<=alpha * pu[i][t];

forall(t in 1..nbPeriod)

sum(i in N)(costp[i] * p[i][t]) <= K; 226

forall(i in N, j in M, t in 1..nbPeriod)

w[i][j][t] + MM*x[i][j][t]<=MM+s[i][t];

forall(i in N, j in M, t in 1..nbPeriod)

-w[i][j][t] + MM*x[i][j][t]<=MM-s[i][t];

forall(i in N, j in M, t in 1..nbPeriod)

w[i][j][t] - MM*x[i][j][t]<=0;

forall(i in N, j in JIT, t in 1..nbPeriod)

z[i][t] + p[i][t] >= d_hat[i][j][t]*y[i][j][t];

forall(i in N, t in 1..nbPeriod)

sum(j in M)(-x[i][j][t] * d_bar[i][j][t]) + gama2[i][t]*z[i][t]

+ sum(j in JIT)p2[i][j][t] <= -s[i][t];

forall(i in N, j in JD, t in 1..nbPeriod)

mio_hat[i][j][t] + noo <=d_hat[i][j][t]*x[i][j][t];

forall(i in N, j in M, t in 1..nbPeriod)

-y[i][j][t] <= x[i][j][t];

forall(i in N, j in M, t in 1..nbPeriod)

y[i][j][t] >= x[i][j][t];

}

227

APPENDIX B: SIMPLEX CODE USED IN PRICING AND PLANNING

MODULE

#include

#define CMAX 10 //max. number of variables in economic function

#define VMAX 10 //max. number of constraints

int NC, NV, NOPTIMAL,P1,P2,XERR;

double TS[CMAX][VMAX];

void Data() {

double R1,R2;

char R;

int I,J;

printf("\n LINEAR PROGRAMMING\n\n");

printf(" MAXIMIZE (Y/N) ? "); scanf("%c", &R);

printf("\n NUMBER OF VARIABLES OF ECONOMIC FUNCTION ? "); scanf("%d", &NV);

printf("\n NUMBER OF CONSTRAINTS ? "); scanf("%d", &NC);

if (R == 'Y' || R=='y')

R1 = 1.0;

else

R1 = -1.0;

printf("\n INPUT COEFFICIENTS OF ECONOMIC FUNCTION:\n");

for (J = 1; J<=NV; J++) { 228

printf(" #%d ? ", J); scanf("%lf", &R2);

TS[1][J+1] = R2 * R1;

}

printf(" Right hand side ? "); scanf("%lf", &R2);

TS[1][1] = R2 * R1;

for (I = 1; I<=NC; I++) {

printf("\n CONSTRAINT #%d:\n", I);

for (J = 1; J<=NV; J++) {

printf(" #%d ? ", J); scanf("%lf", &R2);

TS[I + 1][J + 1] = -R2;

}

printf(" Right hand side ? "); scanf("%lf", &TS[I+1][1]);

}

printf("\n\n RESULTS:\n\n");

for(J=1; J<=NV; J++) TS[0][J+1] = J;

for(I=NV+1; I<=NV+NC; I++) TS[I-NV+1][0] = I;

}

void Pivot();

void Formula();

void Optimize();

void Simplex() { e10: Pivot();

Formula();

Optimize();

if (NOPTIMAL == 1) goto e10; 229

}

void Pivot() {

double RAP,V,XMAX;

int I,J;

XMAX = 0.0;

for(J=2; J<=NV+1; J++) {

if (TS[1][J] > 0.0 && TS[1][J] > XMAX) {

XMAX = TS[1][J];

P2 = J;

}

RAP = 999999.0;

for (I=2; I<=NC+1; I++) {

if (TS[I][P2] >= 0.0) goto e10;

V = fabs(TS[I][1] / TS[I][P2]);

if (V < RAP) {

RAP = V;

P1 = I;

} e10:;}

V = TS[0][P2]; TS[0][P2] = TS[P1][0]; TS[P1][0] = V;

}

void Formula() {; 230

//Labels: e60,e70,e100,e110;

int I,J;

for (I=1; I<=NC+1; I++) {

if (I == P1) goto e70;

for (J=1; J<=NV+1; J++) {

if (J == P2) goto e60;

TS[I][J] -= TS[P1][J] * TS[I][P2] / TS[P1][P2]; e60:;} e70:;}

TS[P1][P2] = 1.0 / TS[P1][P2];

for (J=1; J<=NV+1; J++) {

if (J == P2) goto e100;

TS[P1][J] *= fabs(TS[P1][P2]); e100:;}

for (I=1; I<=NC+1; I++) {

if (I == P1) goto e110;

TS[I][P2] *= TS[P1][P2]; e110:;}

}

void Optimize() {

int I,J;

for (I=2; I<=NC+1; I++)

if (TS[I][1] < 0.0) XERR = 1;

NOPTIMAL = 0;

if (XERR == 1) return; 231

for (J=2; J<=NV+1; J++)

if (TS[1][J] > 0.0) NOPTIMAL = 1;

}

void Results() {

//Labels: e30,e70,e100;

int I,J;

if (XERR == 0) goto e30;

printf(" NO SOLUTION.\n"); goto e100; e30:for (I=1; I<=NV; I++)

for (J=2; J<=NC+1; J++) {

if (TS[J][0] != 1.0*I) goto e70;

printf(" VARIABLE #%d: %f\n", I, TS[J][1]); e70: ;}

printf("\n ECONOMIC FUNCTION: %f\n", TS[1][1]); e100:printf("\n");

}

void main() {

Data();

Simplex();

Results();

}

232

APPENDIX C: WORK PROFILE DATABASE

233

APPENDIX D: MACHINE AND MAINTENANCE DATABASE

234

APPENDIX E: CPLEX CODE FOR INVENTORY MANAGEMENT MODULE

//parameters int m=...; range M=1..m; int s=...; range S=1..s; int nbPeriod = 12; float MM=1000000000;

/////////////////////// float h[M]=...; float a[M][S]=...; float d[M][1..nbPeriod]=...; float p[M][S]=...; float o[M]=...; float l[M][S]=...; float u[M][S]=...; float W=...;

//variable dvar float+ x[M][S][1..nbPeriod]; dvar boolean y[M][S][1..nbPeriod]; dvar float+ q[M][0..nbPeriod];

//model minimize 235

sum(i in M,t in 1..nbPeriod)(h[i]*q[i][t]) + sum(i in M, j in S, t in

1..nbPeriod)(a[i][j]*y[i][j][t]) + sum(i in M, j in S, t in

1..nbPeriod)(p[i][j]*x[i][j][t]);

subject to {

//////////////////////////////////////

forall(i in M)

q[i][0]==0;

forall(i in M, t in 1..nbPeriod-1)

q[i][t+1] - q[i][t] - sum(j in S)x[i][j][t] + d[i][t]==0;

forall(t in 1..nbPeriod)

sum(i in M)o[i]*q[i][t]<=W;

forall(i in M, j in S, t in 1..nbPeriod)

l[i][j]*y[i][j][t]<=x[i][j][t];

forall(i in M, j in S, t in 1..nbPeriod)

x[i][j][t]<=MM*y[i][j][t];

forall(i in M, j in S, t in 1..nbPeriod)

x[i][j][t]<=u[i][j];

} ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

Thesis and Dissertation Services ! !